# 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.

## Relevant Questions

An experiment was conducted to determine the relationship between the amount of warping y for a particular alloy and the temperature (in ° C) under which the experiment was conducted. The sample data appear in the ...A random sample of 22 residential properties was used in a regression of price on nine different independent variables. The variables used in this study were as follows: PRICE = selling price (dollars) BATHS 5 number of ...Refer to Exercise 13.63. a. Explain the apparent inconsistency between the result of part (a) and the results of parts (b) and (c). b. What do you think would happen to the t-value of SQUARE FEET if ROOMS was dropped from ...Refer to Exercise 13.69. a. What is your choice of a good predictive equation? Why did you choose that particular equation? b. The model as constructed does not contain any interaction effects. Construct a model that allows ...The cotton aphid is pale to dark green in cool seasons and yellow in hot, dry summers. Generally distributed throughout temperate, subtropic, and tropic zones, the cotton aphid occurs in all cotton- producing areas of the ...Post your question