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Sam and Hannah, own a restaurant in Edison, New Jersey, and want to study the dining characteristics of their customers. They decide to focus on two variables: the amount of money spent by customers and whether customers order dessert. The results from a sample of 61 customers are as follows:

              Amount spent: Sample mean = $45.83, Sample standard deviation = $6.27

              17 out of the randomly selected 61 customers, purchased dessert.

1. Construct a 98% confidence interval estimate for the population mean amount spent per customer in the restaurant.
2. Construct a 90% confidence interval estimate for the population proportion of customers who purchase dessert.

Their rival Jim owns a competing restaurant. He wishes to conduct a similar survey in his restaurant. However, he does not have access to the information that Sam and Hannah have obtained from the survey they conducted. Jim wants to know the following:

3. What sample size is needed to have 99% confidence of estimating the population mean amount spent in his restaurant to within ±$2.60, assuming that the population standard deviation is estimated to be $9?
4. How many customers need to be selected to have 95%confidence of estimating the population proportion of customers who purchase dessert to within±0.04?

Answer 1

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