Question

number of jobs 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 2.4. part 1 of 4 (a) find the best point estimate of the mean. the best point estimate of the mean is 6.8. part: 1 / 4 part 2 of 4 (b) find the 90% confidence interval of the mean number of jobs. round intermediate and final answers to one decimal place. <μ<

Explanation:

Step1: Find the critical value \( z_{\alpha/2} \)

For a \( 90\% \) confidence interval, \( \alpha=1 - 0.90=0.10 \), and \( \alpha/2=0.05 \).
From the standard normal distribution table, \( z_{\alpha/2}=z_{0.05} = 1.645 \)

Step2: Calculate the margin of error \( E \)

The formula for the margin of error when the population standard deviation \( \sigma \) is known is \( E = z_{\alpha/2}\frac{\sigma}{\sqrt{n}} \)
Given \( \sigma = 2.4 \), \( n = 50 \), and \( z_{\alpha/2}=1.645 \)

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Step3: Calculate the confidence interval

The confidence interval for the population mean \( \mu \) is \( \bar{x}-E<\mu<\bar{x} + E \)
Given \( \bar{x}=6.8 \) and \( E = 0.56 \)

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Answer:

\( 6.2<\mu<7.4 \)