Does sleep deprivation linger for more than a day? Researchers designed a study using 21 volunteer subjects between the ages of 18 and 25. All 21 participants took a computer-based visual discrimination test at the start of the study. Then the subjects were randomly assigned into two groups. The 11 subjects in one group were deprived of sleep for an entire night in a laboratory setting. The 10 subjects in the other group were allowed unrestricted sleep for the night. Both groups were allowed as much sleep as they wanted for the next two nights. On Day 4, all the subjects took the same visual discrimination test on the computer. Researchers recorded the improvement in time (measured in milliseconds) from Day 1 to Day 4 on the test for each subject. The table shows summary statistics for the two groups.

We used software to randomly reassign the 21 subjects to the two groups 100 times, assuming the treatment received doesn’t affect each individual’s time improvement on the test. A dotplot of the simulated difference (Unrestricted − Sleep-deprived) in mean time improvement is shown.

a. Explain why the researchers didn’t let the subjects choose whether to be in the sleep-deprivation group or the unrestricted sleep group.

b. Etimate and interpret the P-value.

c. What conclusion would you make?

d. Based on your conclusion in part (c), could you have made a Type I error or a Type II error? Justify your answer.

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Group Unrestricted sleep Mean SD 19.82 12.17 Sleep-deprived 3.90 14.73