Question

Investigators are interested in whether a new diet lowers total cholesterol in a group of individuals. They take a sample of 28 participants on the new diet. They know that the mean cholesterol level of the general population (µ) is 201 mg/dL, but they do not have information on the standard deviation of the population. The mean total cholesterol level in their sample of participants is 195 mg/dL and their sample has a standard deviation of 9 mg/dL.

Your research question of interest is:

Does the population of people on a new diet have a different mean cholesterol level than the general population?

You will use the information above to complete the question parts below for a one sample 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 values, 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)

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                            [ Select ]                       ["have", "do NOT have"]         enough evidence to conclude that the population of people on a new diet has a different mean cholesterol level than the general population."

Part G: Which of the following represents a 95% confidence interval for the unknown population mean cholesterol level of people on a new diet.

(hint: since the population standard deviation (σ) is unknown, you must use the t-distribution for your confidence interval construction.)

Which of the below represents the best interpretation of the 95% confidence interval you calculated on the previous question for the unknown population mean cholesterol level of people on the new diet?

*note: the actual values for the confidence interval limits are left blank intentionally

a. About 95% of people on the new diet have a cholesterol level between ___ and ___.

b. We are 95% confident that the unknown population mean cholesterol level of people on the new diet falls between ___ and ___.

c. It is guaranteed that the unknown population mean cholesterol level of people on the new diet falls between ___ and ___.

d. We are 95% confident that the sample mean cholesterol level of people on the new diet falls between ___ and ___.

Answer 1