Use the information provided to determine a 95% confidence interval for the population variance. A researcher was interested in the variability in service time (in hours) spent by mechanics fixing the same automotive problem. A random sample was taken resulting in a sample of size 20 from a substantial file of reported experience. The summary statistics are as follows: n = 20, sample mean = 13.8 hours, sample standard deviation = 3.9 hours. Assume service time follows a normal distribution. Round to two decimal places.

The 95% confidence interval for the population variance is (8.80, 32.45).

Step-by-step explanation:

The (1 - α)% confidence interval for the population variance is given as follows:

It is provided that:

n = 20

s = 3.9

Confidence level = 95%

⇒ α = 0.05

Compute the critical values of Chi-square:

*Use a Chi-square table.

Compute the 95% confidence interval for the population variance as follows:

Thus, the 95% confidence interval for the population variance is (8.80, 32.45).

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