Question

A sociologist found that in a sample of 50 retired men, the average number of jobs they had during their lifetimes was 6.8. The population standard deviation is 2.3. Find the

90% confidence interval of the mean number of jobs. Round intermediate and final answers to one decimal place.

Answer 1

A sociologist found that in a sample of n = 50 retired men, the average number of jobs they had during their lifetimes was M = 6.8. The population standard deviation is = 2.3.

For the given data the confidence interval is calculated as:

μ = M ± Z(_M)

where:

M = sample mean
Z = Z statistic determined by the confidence level using the excel formula for normal distribution
_M = standard error = √(²/n)

M = 6.8
Z = 1.645 calculated using the excel formula =NORM.S.INV(0.95)
_M = √(2.3²/50) = 0.33

μ = M ± Z(s_M)
μ = 6.8 ± 1.645*0.33
μ = 6.8 ± 0.535

Thus the Confidence interval is computed as:

CI = [6.3, 7.3]