Question

Katrina wants to estimate the proportion of adult Americans who read at least 10 books last year. To do so, she obtains a simple random sample of 100 adult Americans and constructs a 95% confidence interval. Mathew also wants to estimate the proportion of adult Americans who read at least 10 books last year. He obtains a simple random sample of 400 adult Americans and constructs a 99% confidence level. Assuming both Katrina and Mathew obtained the same point estimate, whose estimate will have the smaller margin of error? (Make sure to answer the following parts)

1) Make up a point estimate for Katrina and Mathew's study. Report the point estimate you used.

2) In order to have the same point estimate, what will be the number of success in Katrina's study? What will be the number of success in Mathew's study?

3) Compute the confidence interval for both person as the problem described. Who has the smaller margin of error? How can you tell?

Answer 1

Hence Mathew's estimate has smaller margin of error.