Question

A sociologist found that in a random sample of 50 retired men, the average number of jobs they had during their lifetime was 7.2. The population standard deviation is 2.1. Assume the population is normally distributed. Find the 99% confidence interval of the mean number of jobs.

Answer 1

To find the 99% confidence interval of the mean number of jobs for retired men, use the formula CI = X ± Z * (σ/√n). Plugging in the values, the 99% confidence interval is approximately (6.435, 7.965).

Step-by-step explanation:

To find the 99% confidence interval of the mean number of jobs, we can use the formula: CI = X ± Z * (σ/√n)

Where:

• X = sample mean = 7.2
• Z = z-score for the desired confidence level = 2.575 (from the z-table)
• σ = population standard deviation = 2.1
• n = sample size = 50

Plugging in the values:

CI = 7.2 ± 2.575 * (2.1/√50)

Simplifying:

CI = 7.2 ± 2.575 * 0.297

CI = 7.2 ± 0.765

The 99% confidence interval of the mean number of jobs is approximately (6.435, 7.965).