Question

You want to estimate the mean repair cost for televisions. the estimate must be within $6 of the population mean. Determine the required sample size to construct a 95% confidence interval for the population mean. Assume the population standard deviation is $20.

Answer 1

Given:

Margin of error(E) = 6

c = confidence level = 95% = 0.95

Population standard deviation

The formula to find the sample size(n) is,

Z is the critical value at given confidence level.

alpha = 1 - c = 0.05

alpha/2 = 0.025

1 - (alpha/2) = 1 - 0.025 = 0.975

Search 0.975 or it's closest value in the middle body of table and then take the corresponding z score.

The z score corresponding to the area 0.975 is 1.96

By plugging all the values in the formula of n,

The required sample size is 43.