Question

Investigators want to assess if there is any difference in total cholesterol level between those on a new exercise regimen and those taking a new oral cholesterol medication. They take a sample of 30 participants on a new exercise regimen, and find they have a mean total cholesterol level of 202 mg/dL and sample standard deviation of 6 mg/dL. They compare these results to a sample of 32 participants on the new oral cholesterol medication (with a mean total cholesterol level of 196 mg/dL and sample standard deviation of 10 mg/dL).

Your research question of interest is:

Does the population of people on the new exercise regimen have a different mean total cholesterol level than the population of people on the new medication?

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 - µ2 = 196", "µ1 - µ2 = 202", "µ1 - µ2 = 0", "µ = 0", "x̄ = 0"]      

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

PART B ANSWER: H₁:                             [ Select ]                       ["µ ≠ 0", "µ1 - µ2 = 0", "µ1 - µ2 ≠ 0", "µ ≠ 202", "x̄ ≠ 196"]      

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

PART C ANSWER:                             [ Select ]                       ["-2.431 and 2.431", "-2.660 and 2.660", "-2.000 and 2.000", "3.460", "-1.259"]      

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

PART D ANSWER:                             [ Select ]                       ["69.07", "42.70", "90.82", "9.84", "2.62"]      

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

PART E ANSWER:                             [ Select ]                       ["0.53", "2.42", "2.11", "6.19", "14.90"]      

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

PART F ANSWER:                             [ Select ]                       ["1.24", "2.84", "4.23", "1.39", "2.11"]      

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

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

Answer 1

Part A: µ1 - µ2 = 0

Part B: µ1 - µ2 ≠ 0

Part C: -2.660 and 2.660

Part D:  pooled variance (s²_p) =69.07

Part E:  estimated standard error of x̄₁ - x̄₂ =2.112

Part F:  t-statistic =2.84

PART G Reject the null