Effect Size — Small (≈ d=0.2)
Sample Size — n = 5
Game 1
| Sample | Mean |
|---|---|
| 1 | 27.200 |
| 2 | 23.400 |
| 3 | 26.600 |
| 4 | 26.000 |
| 5 | 22.000 |
| 6 | 20.000 |
| 7 | 21.400 |
| 8 | 29.200 |
| 9 | 22.400 |
| 10 | 25.200 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 2
| Sample | Mean |
|---|---|
| 1 | 26.800 |
| 2 | 23.000 |
| 3 | 25.600 |
| 4 | 19.600 |
| 5 | 31.200 |
| 6 | 25.800 |
| 7 | 20.000 |
| 8 | 25.000 |
| 9 | 21.800 |
| 10 | 27.200 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #10
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #10, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #10).
Game 3
| Sample | Mean |
|---|---|
| 1 | 27.800 |
| 2 | 28.200 |
| 3 | 29.000 |
| 4 | 25.200 |
| 5 | 23.400 |
| 6 | 23.800 |
| 7 | 23.200 |
| 8 | 21.000 |
| 9 | 21.200 |
| 10 | 23.000 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #7
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #7, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #7).
Game 4
| Sample | Mean |
|---|---|
| 1 | 20.200 |
| 2 | 26.000 |
| 3 | 24.200 |
| 4 | 25.000 |
| 5 | 22.400 |
| 6 | 26.200 |
| 7 | 24.200 |
| 8 | 25.200 |
| 9 | 24.400 |
| 10 | 24.400 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 5
| Sample | Mean |
|---|---|
| 1 | 22.800 |
| 2 | 27.600 |
| 3 | 23.600 |
| 4 | 21.000 |
| 5 | 24.200 |
| 6 | 29.200 |
| 7 | 23.200 |
| 8 | 29.200 |
| 9 | 28.200 |
| 10 | 24.800 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #10
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #10, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #10).
Game 6
| Sample | Mean |
|---|---|
| 1 | 25.200 |
| 2 | 21.600 |
| 3 | 23.000 |
| 4 | 26.200 |
| 5 | 24.000 |
| 6 | 26.200 |
| 7 | 21.400 |
| 8 | 24.600 |
| 9 | 22.200 |
| 10 | 22.000 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #4
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #4, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #4).
Game 7
| Sample | Mean |
|---|---|
| 1 | 23.400 |
| 2 | 25.200 |
| 3 | 23.600 |
| 4 | 26.400 |
| 5 | 23.600 |
| 6 | 23.600 |
| 7 | 26.800 |
| 8 | 22.600 |
| 9 | 17.200 |
| 10 | 25.200 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #7
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #7, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #7).
Game 8
| Sample | Mean |
|---|---|
| 1 | 27.800 |
| 2 | 29.400 |
| 3 | 23.800 |
| 4 | 25.400 |
| 5 | 22.000 |
| 6 | 22.200 |
| 7 | 22.400 |
| 8 | 25.000 |
| 9 | 22.800 |
| 10 | 24.000 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #8
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #8, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #8).
Game 9
| Sample | Mean |
|---|---|
| 1 | 22.000 |
| 2 | 26.800 |
| 3 | 19.600 |
| 4 | 26.200 |
| 5 | 25.400 |
| 6 | 27.400 |
| 7 | 24.800 |
| 8 | 26.600 |
| 9 | 26.200 |
| 10 | 23.000 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #5
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #5, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #5).
Game 10
| Sample | Mean |
|---|---|
| 1 | 19.400 |
| 2 | 25.400 |
| 3 | 22.400 |
| 4 | 21.000 |
| 5 | 22.600 |
| 6 | 24.400 |
| 7 | 23.200 |
| 8 | 23.800 |
| 9 | 25.400 |
| 10 | 20.400 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Sample Size — n = 25
Game 1
| Sample | Mean |
|---|---|
| 1 | 24.840 |
| 2 | 24.680 |
| 3 | 23.280 |
| 4 | 23.720 |
| 5 | 24.480 |
| 6 | 25.840 |
| 7 | 24.200 |
| 8 | 22.280 |
| 9 | 24.040 |
| 10 | 24.000 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 2
| Sample | Mean |
|---|---|
| 1 | 24.040 |
| 2 | 23.760 |
| 3 | 22.480 |
| 4 | 24.320 |
| 5 | 24.040 |
| 6 | 21.960 |
| 7 | 23.080 |
| 8 | 21.440 |
| 9 | 22.080 |
| 10 | 23.840 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #6
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #6, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #6).
Game 3
| Sample | Mean |
|---|---|
| 1 | 24.920 |
| 2 | 26.680 |
| 3 | 22.440 |
| 4 | 23.560 |
| 5 | 23.840 |
| 6 | 24.520 |
| 7 | 23.960 |
| 8 | 23.880 |
| 9 | 22.480 |
| 10 | 21.760 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #2
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #2, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #2).
Game 4
| Sample | Mean |
|---|---|
| 1 | 22.840 |
| 2 | 24.160 |
| 3 | 23.440 |
| 4 | 24.160 |
| 5 | 21.760 |
| 6 | 24.120 |
| 7 | 23.080 |
| 8 | 24.760 |
| 9 | 24.160 |
| 10 | 22.640 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 5
| Sample | Mean |
|---|---|
| 1 | 23.960 |
| 2 | 22.320 |
| 3 | 24.000 |
| 4 | 23.560 |
| 5 | 22.480 |
| 6 | 22.520 |
| 7 | 23.400 |
| 8 | 23.720 |
| 9 | 25.000 |
| 10 | 22.640 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 6
| Sample | Mean |
|---|---|
| 1 | 24.760 |
| 2 | 22.760 |
| 3 | 22.640 |
| 4 | 23.400 |
| 5 | 24.480 |
| 6 | 23.080 |
| 7 | 23.120 |
| 8 | 23.200 |
| 9 | 24.960 |
| 10 | 24.600 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 7
| Sample | Mean |
|---|---|
| 1 | 23.920 |
| 2 | 23.760 |
| 3 | 24.000 |
| 4 | 22.640 |
| 5 | 25.000 |
| 6 | 22.040 |
| 7 | 23.640 |
| 8 | 26.560 |
| 9 | 24.000 |
| 10 | 24.960 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 8
| Sample | Mean |
|---|---|
| 1 | 22.240 |
| 2 | 23.880 |
| 3 | 24.880 |
| 4 | 23.640 |
| 5 | 23.560 |
| 6 | 23.880 |
| 7 | 21.600 |
| 8 | 23.360 |
| 9 | 24.080 |
| 10 | 23.080 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 9
| Sample | Mean |
|---|---|
| 1 | 24.880 |
| 2 | 27.080 |
| 3 | 25.520 |
| 4 | 25.680 |
| 5 | 23.600 |
| 6 | 23.760 |
| 7 | 26.000 |
| 8 | 22.440 |
| 9 | 22.120 |
| 10 | 22.480 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 10
| Sample | Mean |
|---|---|
| 1 | 22.880 |
| 2 | 24.400 |
| 3 | 25.800 |
| 4 | 23.520 |
| 5 | 23.680 |
| 6 | 24.600 |
| 7 | 22.880 |
| 8 | 24.760 |
| 9 | 23.600 |
| 10 | 23.920 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Sample Size — n = 100
Game 1
| Sample | Mean |
|---|---|
| 1 | 24.360 |
| 2 | 23.900 |
| 3 | 24.430 |
| 4 | 23.890 |
| 5 | 23.220 |
| 6 | 24.910 |
| 7 | 23.620 |
| 8 | 23.770 |
| 9 | 23.540 |
| 10 | 24.100 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 2
| Sample | Mean |
|---|---|
| 1 | 24.290 |
| 2 | 23.480 |
| 3 | 23.110 |
| 4 | 23.110 |
| 5 | 24.420 |
| 6 | 23.010 |
| 7 | 25.110 |
| 8 | 24.000 |
| 9 | 24.440 |
| 10 | 23.740 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #9
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #9, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #9).
Game 3
| Sample | Mean |
|---|---|
| 1 | 24.200 |
| 2 | 24.390 |
| 3 | 25.660 |
| 4 | 24.570 |
| 5 | 25.350 |
| 6 | 23.850 |
| 7 | 24.600 |
| 8 | 24.820 |
| 9 | 24.530 |
| 10 | 23.570 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #4
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #4, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #4).
Game 4
| Sample | Mean |
|---|---|
| 1 | 24.430 |
| 2 | 22.890 |
| 3 | 25.010 |
| 4 | 23.950 |
| 5 | 22.810 |
| 6 | 23.120 |
| 7 | 23.710 |
| 8 | 23.740 |
| 9 | 25.280 |
| 10 | 24.710 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #9
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #9, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #9).
Game 5
| Sample | Mean |
|---|---|
| 1 | 23.250 |
| 2 | 24.310 |
| 3 | 23.900 |
| 4 | 23.200 |
| 5 | 23.060 |
| 6 | 24.250 |
| 7 | 23.070 |
| 8 | 23.720 |
| 9 | 24.230 |
| 10 | 25.060 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #10
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #10, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #10).
Game 6
| Sample | Mean |
|---|---|
| 1 | 24.850 |
| 2 | 23.940 |
| 3 | 24.280 |
| 4 | 23.990 |
| 5 | 24.210 |
| 6 | 24.730 |
| 7 | 24.030 |
| 8 | 23.830 |
| 9 | 23.340 |
| 10 | 23.650 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #1
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #1, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #1).
Game 7
| Sample | Mean |
|---|---|
| 1 | 23.350 |
| 2 | 23.240 |
| 3 | 23.510 |
| 4 | 25.130 |
| 5 | 23.590 |
| 6 | 24.220 |
| 7 | 24.480 |
| 8 | 23.270 |
| 9 | 24.090 |
| 10 | 24.190 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 8
| Sample | Mean |
|---|---|
| 1 | 24.910 |
| 2 | 24.720 |
| 3 | 24.890 |
| 4 | 23.970 |
| 5 | 24.140 |
| 6 | 23.590 |
| 7 | 23.400 |
| 8 | 24.270 |
| 9 | 23.660 |
| 10 | 24.270 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 9
| Sample | Mean |
|---|---|
| 1 | 22.920 |
| 2 | 24.530 |
| 3 | 24.230 |
| 4 | 23.460 |
| 5 | 24.890 |
| 6 | 23.140 |
| 7 | 23.640 |
| 8 | 23.910 |
| 9 | 24.700 |
| 10 | 23.620 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 10
| Sample | Mean |
|---|---|
| 1 | 24.480 |
| 2 | 24.670 |
| 3 | 24.820 |
| 4 | 24.140 |
| 5 | 24.940 |
| 6 | 22.960 |
| 7 | 23.650 |
| 8 | 24.690 |
| 9 | 24.780 |
| 10 | 23.940 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #1
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #1, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #1).
Sample Size — n = 1000
Game 1
| Sample | Mean |
|---|---|
| 1 | 24.069 |
| 2 | 23.771 |
| 3 | 24.136 |
| 4 | 24.133 |
| 5 | 23.946 |
| 6 | 23.788 |
| 7 | 25.022 |
| 8 | 24.018 |
| 9 | 23.896 |
| 10 | 24.224 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #7
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #7, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #7).
Game 2
| Sample | Mean |
|---|---|
| 1 | 24.185 |
| 2 | 24.767 |
| 3 | 24.032 |
| 4 | 23.916 |
| 5 | 24.106 |
| 6 | 23.907 |
| 7 | 23.896 |
| 8 | 23.623 |
| 9 | 24.290 |
| 10 | 23.995 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #2
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #2, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #2).
Game 3
| Sample | Mean |
|---|---|
| 1 | 23.938 |
| 2 | 24.069 |
| 3 | 24.170 |
| 4 | 24.111 |
| 5 | 23.991 |
| 6 | 23.499 |
| 7 | 23.934 |
| 8 | 23.871 |
| 9 | 23.915 |
| 10 | 24.283 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 4
| Sample | Mean |
|---|---|
| 1 | 24.306 |
| 2 | 23.187 |
| 3 | 24.237 |
| 4 | 23.989 |
| 5 | 25.227 |
| 6 | 23.765 |
| 7 | 23.624 |
| 8 | 24.393 |
| 9 | 23.806 |
| 10 | 24.184 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #5
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #5, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #5).
Game 5
| Sample | Mean |
|---|---|
| 1 | 23.723 |
| 2 | 24.102 |
| 3 | 23.881 |
| 4 | 23.754 |
| 5 | 24.010 |
| 6 | 23.775 |
| 7 | 24.192 |
| 8 | 23.720 |
| 9 | 24.095 |
| 10 | 23.961 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 6
| Sample | Mean |
|---|---|
| 1 | 24.139 |
| 2 | 24.042 |
| 3 | 23.760 |
| 4 | 25.023 |
| 5 | 23.746 |
| 6 | 23.961 |
| 7 | 24.470 |
| 8 | 24.167 |
| 9 | 24.069 |
| 10 | 23.829 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #4
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #4, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #4).
Game 7
| Sample | Mean |
|---|---|
| 1 | 23.884 |
| 2 | 23.901 |
| 3 | 23.614 |
| 4 | 24.304 |
| 5 | 24.224 |
| 6 | 24.122 |
| 7 | 24.460 |
| 8 | 23.904 |
| 9 | 24.203 |
| 10 | 23.990 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 8
| Sample | Mean |
|---|---|
| 1 | 24.292 |
| 2 | 23.884 |
| 3 | 24.724 |
| 4 | 24.006 |
| 5 | 24.109 |
| 6 | 24.215 |
| 7 | 24.235 |
| 8 | 23.954 |
| 9 | 23.912 |
| 10 | 24.254 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #3
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #3, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #3).
Game 9
| Sample | Mean |
|---|---|
| 1 | 23.710 |
| 2 | 24.508 |
| 3 | 25.049 |
| 4 | 24.104 |
| 5 | 23.932 |
| 6 | 24.043 |
| 7 | 24.251 |
| 8 | 24.090 |
| 9 | 24.089 |
| 10 | 23.566 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #3
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #3, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #3).
Game 10
| Sample | Mean |
|---|---|
| 1 | 24.071 |
| 2 | 24.215 |
| 3 | 23.914 |
| 4 | 24.247 |
| 5 | 23.990 |
| 6 | 23.781 |
| 7 | 23.709 |
| 8 | 24.131 |
| 9 | 23.918 |
| 10 | 23.910 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Effect Size — Medium (≈ d=0.5)
Sample Size — n = 5
Game 1
| Sample | Mean |
|---|---|
| 1 | 22.200 |
| 2 | 26.400 |
| 3 | 18.200 |
| 4 | 21.000 |
| 5 | 20.400 |
| 6 | 22.400 |
| 7 | 22.200 |
| 8 | 24.200 |
| 9 | 19.000 |
| 10 | 22.400 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 2
| Sample | Mean |
|---|---|
| 1 | 22.000 |
| 2 | 21.400 |
| 3 | 20.600 |
| 4 | 22.200 |
| 5 | 20.600 |
| 6 | 23.000 |
| 7 | 22.400 |
| 8 | 24.400 |
| 9 | 20.600 |
| 10 | 15.800 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 3
| Sample | Mean |
|---|---|
| 1 | 26.000 |
| 2 | 22.400 |
| 3 | 23.000 |
| 4 | 28.400 |
| 5 | 26.200 |
| 6 | 21.000 |
| 7 | 25.800 |
| 8 | 28.800 |
| 9 | 22.200 |
| 10 | 22.800 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 4
| Sample | Mean |
|---|---|
| 1 | 23.600 |
| 2 | 22.000 |
| 3 | 20.200 |
| 4 | 25.400 |
| 5 | 25.600 |
| 6 | 24.400 |
| 7 | 25.200 |
| 8 | 26.000 |
| 9 | 22.400 |
| 10 | 24.800 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #6
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #6, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #6).
Game 5
| Sample | Mean |
|---|---|
| 1 | 23.200 |
| 2 | 22.800 |
| 3 | 24.000 |
| 4 | 24.200 |
| 5 | 22.400 |
| 6 | 25.800 |
| 7 | 22.600 |
| 8 | 25.200 |
| 9 | 23.400 |
| 10 | 22.800 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 6
| Sample | Mean |
|---|---|
| 1 | 20.400 |
| 2 | 23.000 |
| 3 | 25.800 |
| 4 | 25.600 |
| 5 | 26.000 |
| 6 | 25.000 |
| 7 | 22.200 |
| 8 | 28.200 |
| 9 | 27.200 |
| 10 | 28.400 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 7
| Sample | Mean |
|---|---|
| 1 | 24.400 |
| 2 | 28.600 |
| 3 | 18.200 |
| 4 | 27.600 |
| 5 | 25.000 |
| 6 | 27.000 |
| 7 | 22.400 |
| 8 | 25.000 |
| 9 | 17.400 |
| 10 | 26.800 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 8
| Sample | Mean |
|---|---|
| 1 | 20.800 |
| 2 | 22.800 |
| 3 | 26.800 |
| 4 | 21.400 |
| 5 | 28.200 |
| 6 | 25.800 |
| 7 | 27.600 |
| 8 | 24.400 |
| 9 | 29.000 |
| 10 | 18.600 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 9
| Sample | Mean |
|---|---|
| 1 | 22.800 |
| 2 | 21.600 |
| 3 | 21.200 |
| 4 | 20.400 |
| 5 | 21.200 |
| 6 | 28.200 |
| 7 | 22.000 |
| 8 | 21.800 |
| 9 | 21.600 |
| 10 | 23.000 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 10
| Sample | Mean |
|---|---|
| 1 | 28.000 |
| 2 | 22.000 |
| 3 | 30.000 |
| 4 | 25.200 |
| 5 | 23.800 |
| 6 | 21.600 |
| 7 | 19.400 |
| 8 | 21.400 |
| 9 | 25.800 |
| 10 | 26.400 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #1
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #1, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #1).
Sample Size — n = 25
Game 1
| Sample | Mean |
|---|---|
| 1 | 23.120 |
| 2 | 23.480 |
| 3 | 22.760 |
| 4 | 24.360 |
| 5 | 22.520 |
| 6 | 24.200 |
| 7 | 26.120 |
| 8 | 23.520 |
| 9 | 26.480 |
| 10 | 23.560 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #9
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #9, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #9).
Game 2
| Sample | Mean |
|---|---|
| 1 | 22.480 |
| 2 | 24.320 |
| 3 | 25.480 |
| 4 | 24.400 |
| 5 | 23.440 |
| 6 | 27.120 |
| 7 | 22.840 |
| 8 | 25.400 |
| 9 | 23.920 |
| 10 | 24.880 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 3
| Sample | Mean |
|---|---|
| 1 | 22.600 |
| 2 | 24.040 |
| 3 | 23.280 |
| 4 | 22.600 |
| 5 | 25.520 |
| 6 | 24.960 |
| 7 | 24.360 |
| 8 | 22.560 |
| 9 | 21.520 |
| 10 | 23.240 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 4
| Sample | Mean |
|---|---|
| 1 | 20.640 |
| 2 | 26.160 |
| 3 | 25.920 |
| 4 | 23.720 |
| 5 | 25.280 |
| 6 | 24.400 |
| 7 | 23.920 |
| 8 | 25.840 |
| 9 | 23.200 |
| 10 | 24.240 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 5
| Sample | Mean |
|---|---|
| 1 | 23.560 |
| 2 | 23.520 |
| 3 | 25.800 |
| 4 | 23.600 |
| 5 | 24.360 |
| 6 | 27.000 |
| 7 | 22.440 |
| 8 | 23.160 |
| 9 | 24.080 |
| 10 | 24.480 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #6
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #6, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #6).
Game 6
| Sample | Mean |
|---|---|
| 1 | 23.720 |
| 2 | 24.720 |
| 3 | 23.120 |
| 4 | 24.040 |
| 5 | 24.440 |
| 6 | 23.480 |
| 7 | 20.560 |
| 8 | 22.920 |
| 9 | 23.320 |
| 10 | 23.160 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 7
| Sample | Mean |
|---|---|
| 1 | 28.680 |
| 2 | 25.920 |
| 3 | 23.280 |
| 4 | 25.440 |
| 5 | 24.160 |
| 6 | 23.600 |
| 7 | 26.160 |
| 8 | 25.880 |
| 9 | 24.520 |
| 10 | 26.280 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #1
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #1, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #1).
Game 8
| Sample | Mean |
|---|---|
| 1 | 23.840 |
| 2 | 23.440 |
| 3 | 24.400 |
| 4 | 24.640 |
| 5 | 26.440 |
| 6 | 24.360 |
| 7 | 23.320 |
| 8 | 23.160 |
| 9 | 26.080 |
| 10 | 24.400 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 9
| Sample | Mean |
|---|---|
| 1 | 23.400 |
| 2 | 23.640 |
| 3 | 25.000 |
| 4 | 25.720 |
| 5 | 24.120 |
| 6 | 22.160 |
| 7 | 22.880 |
| 8 | 26.280 |
| 9 | 23.240 |
| 10 | 23.400 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #8
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #8, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #8).
Game 10
| Sample | Mean |
|---|---|
| 1 | 22.560 |
| 2 | 26.240 |
| 3 | 25.200 |
| 4 | 25.560 |
| 5 | 24.160 |
| 6 | 23.360 |
| 7 | 23.840 |
| 8 | 23.400 |
| 9 | 26.400 |
| 10 | 24.600 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #9
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #9, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #9).
Sample Size — n = 100
Game 1
| Sample | Mean |
|---|---|
| 1 | 24.230 |
| 2 | 24.670 |
| 3 | 25.520 |
| 4 | 23.320 |
| 5 | 23.690 |
| 6 | 23.430 |
| 7 | 27.110 |
| 8 | 24.200 |
| 9 | 23.560 |
| 10 | 24.010 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #7
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #7, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #7).
Game 2
| Sample | Mean |
|---|---|
| 1 | 24.610 |
| 2 | 25.010 |
| 3 | 24.750 |
| 4 | 25.010 |
| 5 | 23.070 |
| 6 | 23.660 |
| 7 | 24.490 |
| 8 | 25.910 |
| 9 | 24.610 |
| 10 | 22.720 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #8
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #8, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #8).
Game 3
| Sample | Mean |
|---|---|
| 1 | 23.510 |
| 2 | 23.220 |
| 3 | 24.850 |
| 4 | 23.270 |
| 5 | 23.050 |
| 6 | 25.200 |
| 7 | 24.920 |
| 8 | 24.180 |
| 9 | 24.770 |
| 10 | 24.370 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 4
| Sample | Mean |
|---|---|
| 1 | 24.650 |
| 2 | 24.430 |
| 3 | 24.280 |
| 4 | 23.920 |
| 5 | 22.810 |
| 6 | 26.270 |
| 7 | 23.790 |
| 8 | 24.760 |
| 9 | 24.080 |
| 10 | 24.160 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #6
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #6, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #6).
Game 5
| Sample | Mean |
|---|---|
| 1 | 23.490 |
| 2 | 23.140 |
| 3 | 23.940 |
| 4 | 24.020 |
| 5 | 23.010 |
| 6 | 25.960 |
| 7 | 22.490 |
| 8 | 24.280 |
| 9 | 23.770 |
| 10 | 23.950 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #6
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #6, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #6).
Game 6
| Sample | Mean |
|---|---|
| 1 | 23.540 |
| 2 | 22.970 |
| 3 | 24.280 |
| 4 | 24.340 |
| 5 | 22.650 |
| 6 | 25.850 |
| 7 | 24.270 |
| 8 | 23.790 |
| 9 | 24.580 |
| 10 | 23.660 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #6
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #6, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #6).
Game 7
| Sample | Mean |
|---|---|
| 1 | 25.080 |
| 2 | 23.590 |
| 3 | 23.690 |
| 4 | 23.450 |
| 5 | 23.730 |
| 6 | 23.810 |
| 7 | 24.390 |
| 8 | 23.550 |
| 9 | 24.150 |
| 10 | 23.240 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 8
| Sample | Mean |
|---|---|
| 1 | 25.150 |
| 2 | 27.000 |
| 3 | 24.130 |
| 4 | 24.180 |
| 5 | 23.950 |
| 6 | 24.110 |
| 7 | 23.780 |
| 8 | 24.090 |
| 9 | 23.660 |
| 10 | 24.100 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #2
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #2, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #2).
Game 9
| Sample | Mean |
|---|---|
| 1 | 24.450 |
| 2 | 24.130 |
| 3 | 23.750 |
| 4 | 24.380 |
| 5 | 23.530 |
| 6 | 24.070 |
| 7 | 24.070 |
| 8 | 22.890 |
| 9 | 24.610 |
| 10 | 24.110 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 10
| Sample | Mean |
|---|---|
| 1 | 25.260 |
| 2 | 23.800 |
| 3 | 24.300 |
| 4 | 24.660 |
| 5 | 24.250 |
| 6 | 24.270 |
| 7 | 23.340 |
| 8 | 24.060 |
| 9 | 24.210 |
| 10 | 23.490 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Sample Size — n = 1000
Game 1
| Sample | Mean |
|---|---|
| 1 | 24.057 |
| 2 | 25.841 |
| 3 | 24.391 |
| 4 | 23.926 |
| 5 | 24.169 |
| 6 | 23.849 |
| 7 | 23.929 |
| 8 | 24.129 |
| 9 | 24.378 |
| 10 | 23.868 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #2
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #2, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #2).
Game 2
| Sample | Mean |
|---|---|
| 1 | 23.827 |
| 2 | 24.066 |
| 3 | 23.811 |
| 4 | 26.073 |
| 5 | 24.021 |
| 6 | 24.454 |
| 7 | 24.210 |
| 8 | 24.170 |
| 9 | 23.952 |
| 10 | 24.244 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #4
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #4, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #4).
Game 3
| Sample | Mean |
|---|---|
| 1 | 24.046 |
| 2 | 23.945 |
| 3 | 23.720 |
| 4 | 23.951 |
| 5 | 24.084 |
| 6 | 23.897 |
| 7 | 23.610 |
| 8 | 24.189 |
| 9 | 24.236 |
| 10 | 23.613 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 4
| Sample | Mean |
|---|---|
| 1 | 23.569 |
| 2 | 23.834 |
| 3 | 24.037 |
| 4 | 24.000 |
| 5 | 24.339 |
| 6 | 23.955 |
| 7 | 24.067 |
| 8 | 23.569 |
| 9 | 23.787 |
| 10 | 23.781 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 5
| Sample | Mean |
|---|---|
| 1 | 24.194 |
| 2 | 23.872 |
| 3 | 23.869 |
| 4 | 23.924 |
| 5 | 24.300 |
| 6 | 23.934 |
| 7 | 23.770 |
| 8 | 23.991 |
| 9 | 23.845 |
| 10 | 25.835 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #10
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #10, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #10).
Game 6
| Sample | Mean |
|---|---|
| 1 | 24.055 |
| 2 | 24.290 |
| 3 | 23.716 |
| 4 | 24.131 |
| 5 | 23.775 |
| 6 | 23.766 |
| 7 | 23.884 |
| 8 | 24.204 |
| 9 | 24.151 |
| 10 | 24.027 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 7
| Sample | Mean |
|---|---|
| 1 | 23.593 |
| 2 | 24.262 |
| 3 | 24.002 |
| 4 | 23.717 |
| 5 | 24.036 |
| 6 | 24.279 |
| 7 | 24.150 |
| 8 | 24.154 |
| 9 | 25.918 |
| 10 | 24.292 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #9
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #9, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #9).
Game 8
| Sample | Mean |
|---|---|
| 1 | 24.098 |
| 2 | 24.017 |
| 3 | 24.385 |
| 4 | 24.321 |
| 5 | 24.022 |
| 6 | 23.955 |
| 7 | 23.985 |
| 8 | 23.819 |
| 9 | 24.052 |
| 10 | 23.990 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 9
| Sample | Mean |
|---|---|
| 1 | 26.007 |
| 2 | 24.070 |
| 3 | 23.641 |
| 4 | 24.343 |
| 5 | 24.176 |
| 6 | 24.070 |
| 7 | 23.920 |
| 8 | 23.668 |
| 9 | 24.102 |
| 10 | 24.101 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #1
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #1, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #1).
Game 10
| Sample | Mean |
|---|---|
| 1 | 24.031 |
| 2 | 24.168 |
| 3 | 23.840 |
| 4 | 24.343 |
| 5 | 23.954 |
| 6 | 24.006 |
| 7 | 24.061 |
| 8 | 23.898 |
| 9 | 23.655 |
| 10 | 26.030 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #10
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #10, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #10).
Effect Size — Large (≈ d=0.8)
Sample Size — n = 5
Game 1
| Sample | Mean |
|---|---|
| 1 | 19.200 |
| 2 | 26.800 |
| 3 | 24.800 |
| 4 | 24.600 |
| 5 | 27.000 |
| 6 | 17.600 |
| 7 | 23.400 |
| 8 | 20.400 |
| 9 | 25.600 |
| 10 | 19.400 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 2
| Sample | Mean |
|---|---|
| 1 | 24.200 |
| 2 | 22.400 |
| 3 | 23.000 |
| 4 | 21.200 |
| 5 | 23.200 |
| 6 | 22.000 |
| 7 | 22.000 |
| 8 | 23.000 |
| 9 | 27.800 |
| 10 | 27.000 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #5
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #5, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #5).
Game 3
| Sample | Mean |
|---|---|
| 1 | 27.000 |
| 2 | 23.200 |
| 3 | 25.800 |
| 4 | 23.400 |
| 5 | 23.400 |
| 6 | 24.200 |
| 7 | 22.200 |
| 8 | 23.600 |
| 9 | 24.400 |
| 10 | 23.600 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 4
| Sample | Mean |
|---|---|
| 1 | 29.200 |
| 2 | 24.400 |
| 3 | 25.800 |
| 4 | 23.200 |
| 5 | 29.000 |
| 6 | 23.800 |
| 7 | 21.800 |
| 8 | 25.400 |
| 9 | 26.200 |
| 10 | 21.200 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 5
| Sample | Mean |
|---|---|
| 1 | 23.600 |
| 2 | 25.200 |
| 3 | 24.800 |
| 4 | 23.800 |
| 5 | 21.000 |
| 6 | 22.400 |
| 7 | 26.600 |
| 8 | 23.200 |
| 9 | 30.400 |
| 10 | 25.200 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #9
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #9, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #9).
Game 6
| Sample | Mean |
|---|---|
| 1 | 19.000 |
| 2 | 29.600 |
| 3 | 26.600 |
| 4 | 21.600 |
| 5 | 19.600 |
| 6 | 22.800 |
| 7 | 24.000 |
| 8 | 22.000 |
| 9 | 25.200 |
| 10 | 25.200 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 7
| Sample | Mean |
|---|---|
| 1 | 22.600 |
| 2 | 26.600 |
| 3 | 23.600 |
| 4 | 26.000 |
| 5 | 23.600 |
| 6 | 22.800 |
| 7 | 26.600 |
| 8 | 18.600 |
| 9 | 22.600 |
| 10 | 29.000 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #2
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #2, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #2).
Game 8
| Sample | Mean |
|---|---|
| 1 | 18.200 |
| 2 | 25.000 |
| 3 | 21.800 |
| 4 | 21.600 |
| 5 | 26.800 |
| 6 | 26.000 |
| 7 | 18.800 |
| 8 | 23.800 |
| 9 | 26.200 |
| 10 | 27.600 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 9
| Sample | Mean |
|---|---|
| 1 | 23.600 |
| 2 | 24.000 |
| 3 | 24.800 |
| 4 | 26.400 |
| 5 | 23.800 |
| 6 | 26.400 |
| 7 | 23.400 |
| 8 | 25.400 |
| 9 | 26.400 |
| 10 | 24.200 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 10
| Sample | Mean |
|---|---|
| 1 | 28.400 |
| 2 | 22.400 |
| 3 | 21.200 |
| 4 | 21.600 |
| 5 | 24.600 |
| 6 | 27.200 |
| 7 | 23.200 |
| 8 | 28.000 |
| 9 | 24.600 |
| 10 | 24.600 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Sample Size — n = 25
Game 1
| Sample | Mean |
|---|---|
| 1 | 22.640 |
| 2 | 26.080 |
| 3 | 24.360 |
| 4 | 26.240 |
| 5 | 24.440 |
| 6 | 23.400 |
| 7 | 25.240 |
| 8 | 24.560 |
| 9 | 23.480 |
| 10 | 25.640 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 2
| Sample | Mean |
|---|---|
| 1 | 24.760 |
| 2 | 24.360 |
| 3 | 22.240 |
| 4 | 24.800 |
| 5 | 24.800 |
| 6 | 24.000 |
| 7 | 23.120 |
| 8 | 23.120 |
| 9 | 26.680 |
| 10 | 23.120 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 3
| Sample | Mean |
|---|---|
| 1 | 24.160 |
| 2 | 24.320 |
| 3 | 23.280 |
| 4 | 22.400 |
| 5 | 23.440 |
| 6 | 23.240 |
| 7 | 27.720 |
| 8 | 24.200 |
| 9 | 25.240 |
| 10 | 24.640 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #7
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #7, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #7).
Game 4
| Sample | Mean |
|---|---|
| 1 | 23.800 |
| 2 | 23.720 |
| 3 | 25.200 |
| 4 | 24.440 |
| 5 | 23.400 |
| 6 | 22.600 |
| 7 | 22.960 |
| 8 | 23.920 |
| 9 | 24.080 |
| 10 | 22.240 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 5
| Sample | Mean |
|---|---|
| 1 | 23.280 |
| 2 | 23.840 |
| 3 | 24.720 |
| 4 | 22.560 |
| 5 | 22.360 |
| 6 | 23.160 |
| 7 | 25.440 |
| 8 | 22.200 |
| 9 | 24.400 |
| 10 | 26.720 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #10
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #10, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #10).
Game 6
| Sample | Mean |
|---|---|
| 1 | 23.560 |
| 2 | 23.200 |
| 3 | 24.760 |
| 4 | 23.920 |
| 5 | 22.760 |
| 6 | 23.120 |
| 7 | 24.680 |
| 8 | 24.440 |
| 9 | 24.880 |
| 10 | 24.240 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 7
| Sample | Mean |
|---|---|
| 1 | 27.040 |
| 2 | 22.840 |
| 3 | 27.000 |
| 4 | 24.400 |
| 5 | 24.440 |
| 6 | 24.880 |
| 7 | 23.080 |
| 8 | 22.680 |
| 9 | 24.280 |
| 10 | 22.440 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #3
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #3, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #3).
Game 8
| Sample | Mean |
|---|---|
| 1 | 22.680 |
| 2 | 24.320 |
| 3 | 22.920 |
| 4 | 25.440 |
| 5 | 22.800 |
| 6 | 20.880 |
| 7 | 22.800 |
| 8 | 25.520 |
| 9 | 23.920 |
| 10 | 22.880 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #8
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #8, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #8).
Game 9
| Sample | Mean |
|---|---|
| 1 | 24.680 |
| 2 | 22.680 |
| 3 | 23.080 |
| 4 | 28.120 |
| 5 | 24.960 |
| 6 | 23.520 |
| 7 | 24.360 |
| 8 | 23.840 |
| 9 | 24.760 |
| 10 | 24.640 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #4
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #4, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #4).
Game 10
| Sample | Mean |
|---|---|
| 1 | 25.640 |
| 2 | 22.400 |
| 3 | 22.200 |
| 4 | 27.040 |
| 5 | 25.080 |
| 6 | 23.400 |
| 7 | 25.640 |
| 8 | 23.280 |
| 9 | 24.560 |
| 10 | 25.120 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #4
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #4, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #4).
Sample Size — n = 100
Game 1
| Sample | Mean |
|---|---|
| 1 | 24.270 |
| 2 | 23.920 |
| 3 | 23.570 |
| 4 | 23.970 |
| 5 | 24.470 |
| 6 | 24.320 |
| 7 | 24.250 |
| 8 | 22.860 |
| 9 | 23.170 |
| 10 | 23.940 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 2
| Sample | Mean |
|---|---|
| 1 | 24.150 |
| 2 | 23.020 |
| 3 | 24.820 |
| 4 | 24.100 |
| 5 | 24.880 |
| 6 | 26.390 |
| 7 | 22.850 |
| 8 | 23.230 |
| 9 | 23.970 |
| 10 | 24.010 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #6
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #6, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #6).
Game 3
| Sample | Mean |
|---|---|
| 1 | 23.320 |
| 2 | 24.120 |
| 3 | 26.880 |
| 4 | 24.250 |
| 5 | 23.680 |
| 6 | 24.520 |
| 7 | 23.960 |
| 8 | 23.710 |
| 9 | 23.400 |
| 10 | 24.380 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #3
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #3, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #3).
Game 4
| Sample | Mean |
|---|---|
| 1 | 24.290 |
| 2 | 24.060 |
| 3 | 23.340 |
| 4 | 26.160 |
| 5 | 24.240 |
| 6 | 23.550 |
| 7 | 23.700 |
| 8 | 24.190 |
| 9 | 24.040 |
| 10 | 24.420 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #4
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #4, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #4).
Game 5
| Sample | Mean |
|---|---|
| 1 | 24.030 |
| 2 | 24.440 |
| 3 | 24.020 |
| 4 | 24.290 |
| 5 | 24.600 |
| 6 | 24.310 |
| 7 | 25.080 |
| 8 | 24.180 |
| 9 | 23.230 |
| 10 | 23.370 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 6
| Sample | Mean |
|---|---|
| 1 | 23.970 |
| 2 | 23.940 |
| 3 | 23.380 |
| 4 | 25.440 |
| 5 | 23.350 |
| 6 | 23.560 |
| 7 | 23.310 |
| 8 | 24.760 |
| 9 | 22.530 |
| 10 | 24.510 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 7
| Sample | Mean |
|---|---|
| 1 | 24.160 |
| 2 | 23.140 |
| 3 | 24.940 |
| 4 | 23.950 |
| 5 | 25.230 |
| 6 | 24.430 |
| 7 | 23.280 |
| 8 | 24.530 |
| 9 | 23.110 |
| 10 | 26.940 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #10
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #10, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #10).
Game 8
| Sample | Mean |
|---|---|
| 1 | 23.440 |
| 2 | 23.820 |
| 3 | 23.000 |
| 4 | 24.060 |
| 5 | 23.460 |
| 6 | 25.020 |
| 7 | 23.940 |
| 8 | 23.240 |
| 9 | 24.840 |
| 10 | 23.230 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 9
| Sample | Mean |
|---|---|
| 1 | 27.040 |
| 2 | 23.920 |
| 3 | 23.720 |
| 4 | 24.340 |
| 5 | 24.530 |
| 6 | 23.810 |
| 7 | 23.700 |
| 8 | 23.660 |
| 9 | 23.560 |
| 10 | 24.140 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #1
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #1, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #1).
Game 10
| Sample | Mean |
|---|---|
| 1 | 24.210 |
| 2 | 23.440 |
| 3 | 24.730 |
| 4 | 23.820 |
| 5 | 23.750 |
| 6 | 23.830 |
| 7 | 24.470 |
| 8 | 24.490 |
| 9 | 23.410 |
| 10 | 27.250 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #10
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #10, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #10).
Sample Size — n = 1000
Game 1
| Sample | Mean |
|---|---|
| 1 | 23.979 |
| 2 | 24.160 |
| 3 | 24.095 |
| 4 | 26.823 |
| 5 | 24.070 |
| 6 | 24.001 |
| 7 | 24.250 |
| 8 | 23.943 |
| 9 | 24.104 |
| 10 | 24.187 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #4
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #4, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #4).
Game 2
| Sample | Mean |
|---|---|
| 1 | 23.927 |
| 2 | 23.697 |
| 3 | 23.881 |
| 4 | 23.881 |
| 5 | 24.148 |
| 6 | 23.789 |
| 7 | 23.910 |
| 8 | 23.879 |
| 9 | 23.850 |
| 10 | 27.097 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #10
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #10, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #10).
Game 3
| Sample | Mean |
|---|---|
| 1 | 24.159 |
| 2 | 23.759 |
| 3 | 23.795 |
| 4 | 23.870 |
| 5 | 24.164 |
| 6 | 23.642 |
| 7 | 23.968 |
| 8 | 23.958 |
| 9 | 23.840 |
| 10 | 23.968 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 4
| Sample | Mean |
|---|---|
| 1 | 23.977 |
| 2 | 23.843 |
| 3 | 24.168 |
| 4 | 23.954 |
| 5 | 24.098 |
| 6 | 23.805 |
| 7 | 26.969 |
| 8 | 24.134 |
| 9 | 23.817 |
| 10 | 24.107 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #7
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #7, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #7).
Game 5
| Sample | Mean |
|---|---|
| 1 | 23.811 |
| 2 | 23.921 |
| 3 | 24.294 |
| 4 | 23.821 |
| 5 | 24.160 |
| 6 | 23.942 |
| 7 | 23.923 |
| 8 | 24.094 |
| 9 | 27.196 |
| 10 | 24.112 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #9
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #9, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #9).
Game 6
| Sample | Mean |
|---|---|
| 1 | 23.613 |
| 2 | 23.808 |
| 3 | 24.238 |
| 4 | 24.083 |
| 5 | 24.138 |
| 6 | 23.954 |
| 7 | 23.941 |
| 8 | 24.049 |
| 9 | 24.301 |
| 10 | 23.998 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 7
| Sample | Mean |
|---|---|
| 1 | 24.414 |
| 2 | 23.720 |
| 3 | 24.067 |
| 4 | 23.936 |
| 5 | 23.891 |
| 6 | 23.976 |
| 7 | 24.388 |
| 8 | 23.730 |
| 9 | 24.042 |
| 10 | 24.388 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 8
| Sample | Mean |
|---|---|
| 1 | 23.710 |
| 2 | 23.918 |
| 3 | 23.980 |
| 4 | 23.902 |
| 5 | 23.756 |
| 6 | 23.843 |
| 7 | 23.798 |
| 8 | 27.104 |
| 9 | 23.874 |
| 10 | 24.428 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #8
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #8, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #8).
Game 9
| Sample | Mean |
|---|---|
| 1 | 23.947 |
| 2 | 23.980 |
| 3 | 23.886 |
| 4 | 23.899 |
| 5 | 24.282 |
| 6 | 24.248 |
| 7 | 24.339 |
| 8 | 23.814 |
| 9 | 24.140 |
| 10 | 23.809 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Retain Null in all cases
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked “None of the Samples”, that was the correct decision. Otherwise, you made a “Type I Error” by rejecting the null hypothesis when in fact it was true.
Game 10
| Sample | Mean |
|---|---|
| 1 | 23.932 |
| 2 | 26.878 |
| 3 | 24.026 |
| 4 | 24.400 |
| 5 | 24.380 |
| 6 | 23.747 |
| 7 | 24.183 |
| 8 | 24.183 |
| 9 | 24.031 |
| 10 | 24.000 |
Decision prompt: Which sample, if any, should lead you to reject the null hypothesis? Or should the null be retained for all ten?
Answer: Reject Sample #2
Hypothesis Testing Decision Matrix (for this pretend scenario):
If you picked Sample #2, that was the correct decision. Otherwise, you made a “Type II Error” by failing to reject the null when it was false (for Sample #2).
Methodology & Notes
Population. Scores are integers from 5 to 35. We simulate a truncated normal so the truncated population has mean μ = 24 and SD = 6. Samples are independently drawn with the same truncation and integer rounding.
Effect sizes. For Small, Medium, and Large we shift exactly one sample’s underlying mean by approximately d = 0.2, 0.5, 0.8 (i.e., +1.2, +3.0, +4.8 on this scale). In roughly half of the games, no sample is shifted.
Output. Each game shows only a 2-column table of Sample and Mean, a decision prompt, the answer, and a short hypothesis-testing feedback message for this pretend scenario. Values are shown to three decimals.