Question

A simple random sample of 60 items resulted in a sample mean of 89. The population standard deviation is 12.

a. Compute the 95% confidence interval for the population mean (to 1 decimal).

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).

Answer 1

Confidence interval = Z*

= 89

= 12

For 95% confidence level, Z* = 1.96

a) Sample size, n = 60

Confidence interval = 89 1.96 x

= 89 3.0

= [86.0, 92.0]

b) Sample size, n = 120

Confidence interval = 89 1.96 x

= 89 2.15

= [86.85, 91.15]