Question

This question has 10 parts. Each of the 10 parts (Part A - Part J) has a dropdown list of possible answers. Choose the best answer from the dropdown list for EACH part of the question below.

A group of psychiatrists want to investigate if there is any difference in depression levels (measured on a scale from [0=not at all depressed] to [100=severely depressed]) in patients who have been treated for depression by being told to regularly exercise versus those who were given an oral medication, Contentica, to treat depression.

The researchers selected a sample of 15 patients who were told to regularly exercise and found that their mean depression level was a score of 48 with a standard deviation of 9.

The researchers also selected a sample of 14 patients who were given the medication Contentica and found that their mean depression level was a score of 54 with a standard deviation of 10.

Conduct an appropriate two-tailed hypothesis test (two independent samples t-test) on whether or not patients who regularly exercise have a different depression level than those who are prescribed the medication Contentica using an alpha (α) level of 0.01.

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

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

PART A ANSWER: H₀:                            [ Select ]                       ["μ1 = 15", "μ1 - μ2 = 0", "μ1 - μ2 = 54", "μ1 - μ2 = 48", "μ1 - μ2 ≠ 48"]      

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

PART B ANSWER: H₁:                            [ Select ]                       ["μ1 - μ2 ≠ 48", "μ1 - μ2 ≠ 14", "μ1 - μ2 ≠ 54", "μ1 ≠ 15", "μ1 - μ2 ≠ 0"]      

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

PART C ANSWER:                            [ Select ]                       ["21", "45", "10", "27", "54"]      

Part D: Which of the following represents the appropriate critical value(s), testing at an alpha level (α) of 0.01?

PART D ANSWER:                            [ Select ]                       ["-2.892 and 2.892", "-2.771 and 2.771", "-2.312 and 2.312", "-1.251 and 1.251", "3.85"]      

Part E: What is the pooled variance (s²_p) associated with your test? (rounded to the nearest hundredth)

PART E ANSWER:                             [ Select ]                       ["45.12", "315.81", "90.15", "76.43", "12.86"]      

Part F: What is the estimated standard error of x̄₁ - x̄₂ associated with your test? (rounded to the nearest hundredth)

PART F ANSWER:                             [ Select ]                       ["3.53", "4.16", "7.89", "2.98", "1.05"]      

Part G: What is the t-statistic associated with your test? (rounded to the nearest hundredth)

PART G ANSWER:                             [ Select ]                       ["1.21", "5.47", "3.96", "2.85", "-1.70"]      

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

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

Part I: 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 patients who regularly exercise do appear to have a different depression level than those who are prescribed the medication Contentica."

Part J: Which of the below represents a 99% confidence interval for the difference between the unknown population mean cholesterol levels of people on the new exercise regimen and people on the new medication?

PART J ANSWER:                             [ Select ]                       ["[-18.28 to -3.16]", "[-15.78 to 3.78]", "[-7.39 to 1.05]", "[-12.81 to 10.45]", "[3.45 to 9.82]"]      

Answer 1