Question

A study is conducted to assess whether residents in City A spent a different out-of-pocket amount on prescription medications from residents in City B last year. The study is restricted to residents who are 50 years of age or older. Residents are selected at random. For each resident, the total amount of dollars spent on prescription medications over the last year is recorded. The summary statistics of the sample data are given in the table below. Let µ1 be the mean out-of-pocket amount that residents in City A spent, and µ2 be the mean out-of-pocket amount that residents in City B spent. Run a two-sample t-test assuming equal variances. Use a significance level of 0.05. City Sample size Sample mean Sample standard deviation A 48 402 50 B 34 387 41

a. Write down the null hypothesis. (5 points)

b. Write down the alternative hypothesis. (5 points)

c. Calculate the point estimate for µ1 − µ2. (5 points)

d. Calculate the pooled sample variance. (10 points)

e. Calculate the standard error of the point estimate in c. (10 points)

f. Calculate the test statistic. (10 points)

g. Find out the critical value. (5 points)

h. Is there a statistically significant difference in the out-of-pocket amount spent on prescription medications between City A and City B? (5 points)

Answer 1