Question

A researcher is interested in hamster wheel-running activity during the summer versus the winter. She suspects that either the hamsters will run less during the winter to conserve energy or they will run more to keep warm. She records the activity of n = 25 hamsters during June, July, and August and compares their running-wheel revolutions per hour to the activity of the same hamsters during December, January, and February.

The data are collected, and the results show an average difference score of M D = 5. 7 and a sum of squares of SS = 2,851.44.

1. What is the value for degrees of freedom for this repeated-measures t test?

2. What is the sample standard deviation (s) for the D scores? (one decimal)

3. What is the estimated standard error of the mean difference (S M D) for this study? (two decimals)

Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis H_0: µ_D = 0 (the null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed.

Observation	A	B
1	1	3
2	3	4
3	5	7
4	4	4
5	8	9

4. What is the M_D? (one decimal)

Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis H_0: µ_D = 0 (the null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed.

Observation	A	B
1	1	3
2	3	4
3	5	7
4	4	4
5	8	9

5. For a repeated-measures t test, you need to calculate the t statistic, which requires you to calculate s and S_MD· What is the estimated standard deviation of the difference scores? (four decimals)

6. For a repeated-measures t test, you need to calculate the t statistic, which requires you to calculate s and S_MD· What is the estimated standard error of the mean difference scores? (Note: For best results, retain at least six decimal places from your calculation of s.) (round your answer to this question to four decimals)

7.What is the t statistic for the repeated-measures t test to test the null hypothesis H₀: µ_D = 0? (two decimals)

Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis H_0: µ_D = 0 (the null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed.

Observation	A	B
1	1	3
2	3	4
3	5	7
4	4	4
5	8	9

You conduct a two-tailed test at α = .05. To find the critical value (in the table) you first need to get the degrees of freedom, which is                            [ Select ]                       ["3", "4", "5"]          

The critical values (the values for t-scores that separate the tails from the main body of the distribution, forming the critical region) are ± _______   

a.) 2.571 b.) "2.776 c.) 3.18   d.) 4.032  

Based on this our finding __________ ["is", "is not"]         significant and we _______ ["reject", "fail to reject"]         the null hypothesis.

Previous studies have shown that playing video games can increase visual perception abilities on tasks presented in the gaming zone of the screen (within 5 degrees of the center). A graduate student is interested in whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone. For her study, she selects a random sample of 64 adults. The subjects complete a difficult spatial perception task to determine baseline levels of their abilities. After playing an action video game (a first-person combat simulation) for 1 hour a day over 10 days, they complete the difficult perception task for a second time.

Before playing the action video game, the mean score in their accuracy on the spatial task was 0.42. After playing the action video game, the mean score was -0.08. The mean of the differences between each person's pre- and post­scores was 0.5, with a standard deviation of the differences equal to 2.4.

The graduate student has no presupposed assumptions about whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone, so she formulates the null and alternative hypotheses as:

H_0: μ D = 0

H_R: μ D ≠ 0

She uses a repeated-measures t test. Because the sample size is large, if the null hypothesis is true as an equality, the test statistic follows a t-distribution with degree of freedom =                            [ Select ]                       ["48", "63", "128", ""]         .

This is a                            [ Select ]                       ["one-tailed", "two-tailed"]         test.

From the table we find that the critical score(s) for the level of significance α = .01 is                            [ Select ]                       ["2.660", "1.671", "2.617", "2.704"]      

In order to calculate the test statistic t, you will need to calculate the estimated standard error first, which is                            [ Select ]                       [".1667", ".2567", "0.3000"]         The calculated test statistic is therefore t =                            [ Select ]       ["-1.67", "+1.67", "-1.94", "+1.94", "-2.99", "+2.99"]          

Answer 1

n = sample size = 25

Sample mean difference = = 5.7Sum of squares = SS = 2851.44

1)

Degrees of freedom = n - 1 = 25 - 1 = 24

Degrees of freedom for the repeated-measures t test = 24

2)

Standard deviation of D scores:

(Round to one decimal)

Sample standard deviation for D scores = 118.8

3)

Estimated standard error of the mean difference is

SE = 23.76 (Round to 2 decimal)

Estimated standard error of the mean difference is 23.76

4)

n = 5

A	B	D=B-A
1	3	2
3	4	1
5	7	2
4	4	0
8	9	1