Question: A home furnishings store that sells bedroom furniture is conducting an end-of-month inventory of the beds (mattress, bed spring, and frame) in stock. An auditor for the store wants to estimate the mean value of the beds in stock at that time. She wants to have 99% confidence that her estimate of the mean value is correct to within $100. On the basis of past experience, she estimates that the standard deviation of the value of a bed is $200.
a. What sample size should she select?
b. Using the sample size selected in (a), an audit was conducted, with the following results:
X¯ = $1,654.27 S = $184.62
Construct a 99% confidence interval estimate of the total value of the beds in stock at the end of the month if there were 258 beds in stock.