Question

A survey was conducted to estimate the mean number of books (denoted by μ) each university student read in the last year. Among a random sample of 61 students, the number of books each student read in the last year was recorded. The sample mean was 7.098 and the sample standard deviation was 2.644.

1. Write down the point estimate of μ. (5 points)

2. Calculate the standard error of the point estimate in a. (10 points)

3. To construct a 95% two-sided confidence interval for μ, what’s the multiplier to use? (5 points)

4. Calculate the lower endpoint of the 95% two-sided confidence interval for μ. (5 points)

5. Calculate the upper endpoint of the 95% two-sided confidence interval for μ. (5 points)

6. Consider a hypothesis testing problem where the null hypothesis is H0 : μ = 10 and the alternative hypothesis is Ha : μ ≠ 10. Use a significance level of 0.05. Based on the 95% two-sided confidence interval for μ above, what’s your decision about whether to reject H0? Give a brief explanation. (10 points)

7. Suppose you’re asked to conduct a hypothesis testing to show that on average a student read more than 5 books last year. Which pair of hypotheses should be used? (5 points)

   A.H0 :μ=5againstHa :μ̸=5 B.H0 :μ<5againstHa :μ≥5 C.H0 :μ≤5againstHa :μ>5 D.H0 :μ≥5againstHa :μ<5

2

Problem 2

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 40 381 39 B 52 422 45

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

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

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

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

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

6. Calculate the test statistic. (10 points)

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

8. 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