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Consumer products companies design different promotional activities to accomplish different goals. According to a spokesperson for General Mills, the company's cents-off coupon offers are designed to convince people to buy its products, while its refund offers (money returned with proof of repeated purchases) are designed to encourage people to continue buying its products. However, these promotional activities are only effective if consumers participate.

In a survey of 562 randomly selected households in the Research Triangle Area (Raleigh, Durham, and Chapel Hill) in 2003, 427 principal shoppers (the person in the household who does the majority of the grocery shopping) indicated that they used cents-off coupons when they went grocery shopping.

a) What is your best estimate of the proportion of households throughout the Research Triangle Area who use cents-off coupons when grocery shopping?

b) Develop a 99% confidence interval for the proportion of households throughout the Research Triangle Area who use cents-off coupons when grocery shopping.

c) Suppose it is desired that the 99% confidence interval be of the form "plus or minus 0.03." How large a sample is required?

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