National Discount has 260 retail outlets throughout the United States. National evaluates each potential location for a

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National Discount has 260 retail outlets throughout the United
States. National evaluates each potential location for a new retail
outlet in part on the mean annual income of the households in the
marketing area o f the new location. National develops an interval
estimate of the mean annual income in a potential marketing area
after taking a random sample of households.
For a marketing area being studied, a sample of 36 households
was taken and the sample mean income was $21,100.39. Based on past
experience, National assumes a known value of s =$4500 for the
population income standard deviation.
A. Develop a 95% confidence interval for the mean annual income
of households in this marketing area. (Round to 2 decimals) The
lower interval is __________ and the upper interval is
________.
B. Suppose that National's management team wants a 95%
confidence interval estimate of the population mean with a margin
of error of E = $500. How large a sample size is needed?