Question

a. Suppose we construct a 99% confidence interval. What are we 99% confident about?

b. Which of the confidence intervals is wider, 90% or 99%?

c. In computing a confidence interval for 𝜇, when do you use the t-distribution and when do you use z, with normal approximation?

d. How does the sample size affect the width of a confidence interval?

Answer 1

Solution

a. Suppose we construct a 99% confidence interval

Conclusion: we are (1−𝛼)100% confident that the true parameter 𝜃 lies in the interval.

                           

b. The 99% CI is wider than 90% CI

c. To computing CI for 𝝁

Case 1: If 𝜎 is known, use 𝑍

                                     

Case 2: If 𝜎 is unknown, 𝑆 is unbiased estimator use (𝑡)

                                 

But only if 𝑛≤30

When 𝑛≥30, we can use 𝑍

                                 

d. How does the sample size affect the width of a confidence interval?