Question

An Atlanta restaurant surveyed 49 diners at random, in order to determine the mean population expenditure at the restaurant for each mean. The restaurant wants to estimate the population mean with 95% confidence level.

Given the following:

X-bar = $49

Population Standard Deviation = $5

Determine the margin of error. Determine the appropriate confidence interval.

Answer 1

n = 49

Confidence level =c =0.95

Here population standard deviation is known so we will use here z interval

Margin of error (E):

Where zc is z critical value for (1+c)/2 = (1+0.95)/2 = 0.975

zc = 1.96            (From statistical table of z values)

E = 1.4

Margin of error is 1.4

95% confidence interval for population mean is

95% confidence interval for population mean is (47.6, 50.4)