Question

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 differentdepression 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

PART A:

Correct option:

H0:   μ1 - μ2 = 0

PART B:

Correct option:

H1:   μ1 - μ2 0

PART C:

Correct option:

"27"

Explanation:
Degrees of Freedom = n1 + n2 - 2 = 15 + 14 - 2 = 27

PART D:

Correct option:

"-2.771 and 2.771"

Explanation:
Degrees of Freedom = 27

= 0.01

Two Tail Test

From Table, critical values of t = 2.771

PART E:

Correct option:

"90.15"

Explanation:

PART F:

Correct option:

"3.53"

Explanation:

PART G:

Correct option:

"-1.70"

Explanation:

t = (48 - 54)/3.53

= - 1.70

PART H:

Correct option:

"Fail to reject (i.e., retain) the null"

Explanation:

Since calculated value of t = - 1.70 is greater than critical value of t = - 2.771, the difference is not significant. Fail to reject null hypothesis.

PART I:

Correct option:

"do NOT have"

PART J:

Correct option:

"[-15.78 to 3.78]"

Explanation:

ndf = 27

= 0.01

From Table, critical values of t = 2.7707

Confidence Interval:
(48 - 54) (2.7707 X 3.53)

= - 6 9.7806

= ( - 15.78 ,3.78)