1 A). A sample survey is designed to estimate the proportion of sports utility vehicles being driven in PEI. A random sample of 500 registrations are selected from a PEI database, and 30 are classified as sports utility vehicles.

Use a 95% confidence interval to estimate the proportion of sports utility vehicles in PEI. (Round your answers to three decimal places.)

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B).A random sample of 60 plain M&Ms contained 13 red candies, and another random sample of 36 peanut M&Ms contained 8 red candies. (Usep₁for the proportion of red candies in plain M&Ms andp₂for the proportion of red candies in peanut M&Ms.)

Construct a 95% confidence interval for the difference in the proportions of red candies for the plain and peanut varieties

(p₁p₂).

(Round your answers to three decimal places.)

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2 Even within a particular chain of hotels, lodging during the summer months can vary substantially depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table. Hotel A Hotel B Hotel C Sample average ($) 145 170 130 Sample standard deviation 17.3 22.9 12.3 (a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel C chains. (Round your answers to two decimal places.) $ to $ (b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Round your answers to two decimal places.) $ to $