Question

Part 1:

Information: A hypothesis of clinical interest was that vitamin C prevents the common cold. A study is organized to test this hypothesis using 20 participants. In the study, 10 were randomly allocated to receive vitamin C capsules and 10 were randomly allocated to receive placebo capsules. The number of colds over a 12-month period for each participant is recorded. The samples were randomly selected, and the populations are approximately normally distributed. Population variances are unknown but assumed to be approximately equal.

In the problems below, you will answer the following question: Is the mean number of colds different between those who take vitamin C and those who do not take vitamin C? (use an α of 0.05)

	The average number of colds	Standard deviation
Vitamin C group:	3.3	1.57
Placebo group:	5.7	1.34

1. State the null hypothesis (2 pts):

2. State the alternative hypothesis (2 pts):

3. What is the appropriate test for this situation? Explain your response! (If applicable, please indicate whether the test is one or two-sided and whether it is a one or two-sample test) (2 pts)

4. What are the degrees-of-freedom (if applicable)? (1 pt)

5. What are the critical values? Note: For two-sided tests, there are two critical values: a positive critical value and a negative critical value. You may use a table or an online calculator to obtain your critical value(s). (3pts)

6. Upon running the calculations, a test statistic is equal (– 3.68). What is your statistical decision – reject the null or fail to reject the null hypothesis? Why? (5 pts)

Part 2:

In 2-4 sentences, explain when would be appropriate to choose the following tests? [Hint: type of variables involved, information the test provides] (2 pts each)

1. Chi-squared test

2. Kaplan-Meier Survival Curve

3. Correlation Analysis

4. Logistic Regression

5. Tukey’s HSD with ANOVA

Answer 1