Question

Number of Jobs A sociologist found that in a random sample of 50 retired men, the average number of jobs they had during their lifetimes was 7.2. The population standard deviation is 2.1. Find the 95% confidence interval of the mean number of jobs.

Answer 1

To find the 95% confidence interval of the mean number of jobs, calculate the margin of error using the formula Margin of Error = Z * (Standard Deviation / sqrt(n)), where Z is the z-score corresponding to the desired confidence level, Standard Deviation is the population standard deviation, and n is the sample size. Once you have the margin of error, calculate the confidence interval by subtracting and adding the margin of error to the sample mean.

Step-by-step explanation:

To find the 95% confidence interval of the mean number of jobs, we first need to calculate the margin of error. The formula for the margin of error is given by:

Margin of Error = Z * (Standard Deviation / sqrt(n))

Where Z is the z-score corresponding to the desired confidence level (in this case, 95%), Standard Deviation is the population standard deviation, and n is the sample size.

Once we have the margin of error, we can calculate the confidence interval by subtracting and adding the margin of error to the sample mean.

Confidence Interval = Sample Mean - Margin of Error to Sample Mean + Margin of Error

Plugging in the values from the given information:

Margin of Error = 1.96 * (2.1 / sqrt(50))

Confidence Interval = 7.2 - Margin of Error to 7.2 + Margin of Error