A lawyer researched the average number of years served by 45 different judges on the Supreme Court. The average number of years served was 13.8 years with a standard deviation of 7.3 years. What is the
95% confidence interval for the average number of years served by all Supreme Court judges?
A) $11.7

Question

A lawyer researched the average number of years served by 45 different judges on the Supreme Court. The average number of years served was 13.8 years with a standard deviation of 7.3 years. What is the
95% confidence interval for the average number of years served by all Supreme Court judges? 
A) $11.7 < \mu < 15.9$
B) $11.8 < \mu < 15.8$
C) $12.9 < \mu < 16.9$
D) $12.5 < \mu < 17.3$

Quizplus · Accepted Answer

The 95% confidence interval is given by:$$\bar{x} \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$$where $\bar{x}$ is the sample mean, $\sigma$ is the population standard deviation, n is the sample size, and $z_{\alpha/2}$ is the critical value from the standard normal distribution corresponding to the desired confidence level.In this case, we have $\bar{x} = 13.8$, $\sigma = 7.3$, n = 45, and $\alpha = 0.05$. Using a standard normal table, we find that $z_{0.025} = 1.96$. Therefore, the 95% confidence interval is:$$13.8 \pm 1.96 \frac{7.3}{\sqrt{45}} = 13.8 \pm 2.6$$$$11.2 < \mu < 16.4$$Therefore, the correct answer is A.

A Lawyer Researched the Average Number of Years Served by 45