Question

This question has 6 parts. Each of the 6 parts (Part A - Part F) has a dropdown list of possible answers. Choose the best answer from the dropdown list for EACH part of the question below.  

The same psychiatrists are now interested in determining if there is any difference in depression levels of participants before and after a group therapy program. Depression levels of a sample of participants both before and after the program are listed below:

Patient #	Depression level before group therapy program (X1)	Depression levels after group therapy program (X2)
1	68	62
2	76	72
3	54	55
4	89	82
5	62	65

You are informed the estimated standard error of the mean differences (s) is 1.96

Using the appropriate two-tailed hypothesis test (a two related samples t-test) with the H₀: µ_D = 0 and H₁: µ_D  ≠ 0, calculate the test statistic and make a decision about the null hypothesis using an alpha (α) level of 0.05.

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

Part A: What is the degrees of freedom (df) associated with your test?

PART A ANSWER:                            [ Select ]                       ["4", "9", "8", "6", "3"]      

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

PART B ANSWER:                            [ Select ]                       ["-4.032", "-2.021 and 2.021", "-1.96 and 1.96", "-2.776 and 2.776", "2.331 and -2.331"]      

Part C: Calculate the sample mean of difference scores which

you will use in the calculation of your test statistic):?

PART C ANSWER:                            [ Select ]                       ["2.1", "3.9", "1.6", "2.6", "3.4"]      

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 D ANSWER:                            [ Select ]                       ["2.92", "2.26", "3.56", "1.97", "1.33"]      

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

PART E ANSWER:                             [ Select ]                       ["Reject the null", "Fail to reject (e.g., retain) the null"]      

Part F: The best interpretation of the appropriate decision regarding the null hypothesis would be: "Based on our study, we                            [ Select ]                       ["have", "do NOT have"]         enough evidence to conclude that there appears to be a difference in the mean depression levels of the population of people before and after the group therapy program."

  

Answer 1

Part A: What is the degrees of freedom =4

Part B: Which of the following represents the appropriate critical value 2.776

Part C: Calculate the sample mean of difference scores =2.6

Part D:What is the t-statistic =1.33

PART E ANSWER Fail to reject  

Part F: do NOT have