Chapter 5.12, Problem 14E

Refer to Exercise 5.14. Suppose the mayor’s staff reviews the proposed survey and decides that in order for the survey to be taken seriously the requirements need to be increased.

1. a. If the level of confidence is increased to 99% with the average rent estimated within $50, how many apartments need to be included in the survey?
2. b. Suppose the budget for the survey will not support increasing the level of confidence to 99%. Provide an explanation to the mayor, who has never taken a statistics course, of the impact on the accuracy of the estimate of the average rent of not raising the level of confidence from 95% to 99%.

5.14 The housing department in a large city monitors the rent for rent-controlled apartments in the city. The mayor wants an estimate of the average rent. The housing department must determine the number of apartments to include in a survey in order to be able to estimate the average rent to within $100 using a 95% confidence interval. From past surveys, the monthly charge for rent-controlled apartments ranged from $1,000 to $3,500. How many renters must be included in the survey to meet the requirements?