Question

Researchers are interested in comparing the depression scores (measured on a scale of 1-100) of patients diagnosed with clinical depression before and after they have participated in a new exercise regimen. They take a random sample of 5 people who report low levels of exercise and measure their depression scores. They then have these 5 patients complete a 4-week exercise regimen and measure their depression scores after the 4 weeks. Results of analysis are presented in the table below.

Participant ID	Depression score before the 4-week exercise regimen	Depression score before the 4-week depression exercise regimen
A	78	69
B	87	82
C	57	56
D	62	63
E	74	72

Your research question of interest is:

Is there a difference in the mean depression score of patients before and after they participate in the 4- week exercise regimen?

You are informed the estimated standard error of the mean differences (s) is 1.74

You will use the information above to complete the question parts below for a two related samples t-test.

Part A: Which of the following represents the appropriate null hypothesis (H₀), given this research question of interest?

Part B: Which of the following represents the appropriate alternative hypothesis (H₁), given this research question of interest?

Part C: Which of the following represents the appropriate critical value(s), testing at an alpha level (α) of 0.05?

Part D: What is the t-statistic associated with your test? (rounded to the nearest hundredth) - see note above for the value of the standard error of the mean differences.

Part E: Given your test results, what is your decision about the null hypothesis?

Part F: The best interpretation of the appropriate decision regarding the null hypothesis would be: "Based on our study, we (Have/Have not)

enough evidence to conclude that there appears to be a difference in the population mean depression score before and after a 4 week exercise regimen."

  

Answer 1