Question: The owner of a restaurant that serves continental food wants to study characteristics of his customers. He decides to focus on two variables: the amount of money spent by customers and whether customers order dessert. The results from a sample of 60 customers are as follows:

- Amount spent: \(\bar{X}=\\) 38.54, S=\$ 7.26$

- 18 customers purchased dessert.

1. Construct a \(95 \%\) confidence interval estimate of the population mean amount spent per customer in the restaurant.
2. Construct a \(90 \%\) confidence interval estimate of the population proportion of customers who purchase dessert. The owner of a competing restaurant wants to conduct a similar survey in her restaurant. This owner does not have access to the information of the owner of the first restaurant. Answer the following questions:
3. What sample size is needed to have \(95 \%\) confidence of estimating the population mean amount spent in her restaurant to within \(\pm \\) 1.50$, assuming that the standard deviation is $8.
4. What sample size is needed to have \(90 \%\) confidence of estimating the population proportion of customers who purchase dessert to within \(\pm 0.04 ?\)
5. Based on your answers to \((\mathrm{c})\) and \((\mathrm{d})\), how large a sample should the owner take?

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