Chapter 8.4, Problem 38E

According to Franchise business review, over 50% of all food franchises earn a profit of less than $50,000 a year. In a sample of 142 casual dining restaurants, 81 earned a profit of less than $50,000 last year.

1. a. What is the point estimate of the proportion of casual dining restaurants that earned a profit of less than $50,000 last year?
2. b. Determine the margin of error and provide a 95% confidence interval for the proportion of casual dining restaurants that earned a profit of less than $50,000 last year.
3. c. How large a sample is needed if the desired margin of error is .03?