# Question: A psychologist wants to examine the effects of sleep deprivation

A psychologist wants to examine the effects of sleep deprivation on a person’s ability to perform simple arithmetic tasks. To do this, prospective subjects are screened to obtain individuals whose daily sleep patterns were closely matched. From this group, 20 subjects are chosen. Each individual selected is randomly assigned to one of five groups, four individuals per group.

Group 1: 0 hours of sleep

Group 2: 2 hours of sleep

Group 3: 4 hours of sleep

Group 4: 6 hours of sleep

Group 5: 8 hours of sleep

All subjects are then placed on a standard routine for the next 24 hours.

The following day after breakfast, each individual is tested to determine the number of arithmetic additions done correctly in a 10- minute period. That evening the amount of sleep each person is allowed depends on the group to which he or she had been assigned. The following morning after breakfast, each person is again tested using a different but equally difficult set of additions.

Let the response of interest be the number of correct responses on the first test day minus the number correct on the second test day. The data are presented here.

Group Response, y

1………………………….. 39, 33, 41, 40

2………………………….. 25, 29, 34, 26

3………………………….. 10, 18, 14, 17

4……………………………… 4, 6, 21, 9

5……………………………. 25, 0, 23, 28

a. Plot the sample data and use the plot to suggest a model.

b. Fit the suggested model.

c. Examine the fitted model for possible violation of assumptions.

Group 1: 0 hours of sleep

Group 2: 2 hours of sleep

Group 3: 4 hours of sleep

Group 4: 6 hours of sleep

Group 5: 8 hours of sleep

All subjects are then placed on a standard routine for the next 24 hours.

The following day after breakfast, each individual is tested to determine the number of arithmetic additions done correctly in a 10- minute period. That evening the amount of sleep each person is allowed depends on the group to which he or she had been assigned. The following morning after breakfast, each person is again tested using a different but equally difficult set of additions.

Let the response of interest be the number of correct responses on the first test day minus the number correct on the second test day. The data are presented here.

Group Response, y

1………………………….. 39, 33, 41, 40

2………………………….. 25, 29, 34, 26

3………………………….. 10, 18, 14, 17

4……………………………… 4, 6, 21, 9

5……………………………. 25, 0, 23, 28

a. Plot the sample data and use the plot to suggest a model.

b. Fit the suggested model.

c. Examine the fitted model for possible violation of assumptions.

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