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} = √(2.3^{2}/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]**

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