Question

A group of investors wants to develop a chain of fast-food restaurants. In determining potential costs for each facility, they must consider, among other expenses, the average monthly electric bill. They decide to sample some fast-food restaurants currently operating to estimate the monthly cost of electricity. They want to be 90% confident of their results and want the error of the estimate to be no more than $120. They estimate that the standard deviation is $475. How large a sample should they take?

Answer 1

Solution :

Given that,

Population standard deviation = = 475

Margin of error = E = 120

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

sample size = n = (Z_/2* / E) ²

n = (1.645 * 475 / 120)²

n = 42.40

n = 43

Sample size = 43