Question

A lawyer researched the average number of years served by 45 different justices 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 estimate for the average number of years served by all Supreme Court justices? Place your limits, rounded to 1 decimal place, in the blanks. Place you lower limit in the first blank.

Answer 1

Answer:
`11.7<\mu<15.9`

Explanation:

Given : Significance level :
`\alpha:1-0.95=0.05`

Sample size : n=45

Critical value :
`z_(\alpha/2)=1.96`

Sample mean :
`\overline{x}=13.8\text{ years}`

Standard deviation :
`\sigma=7.3\text{ years}`

The confidence interval for population mean is given by :-

`\overline{x}\pm z_(\alpha/2)(\sigma)/(√(n))\\\\=13.8\pm(1.96)(7.3)/(√(45))\\\\\approx13.8\pm2.1\\\\=(13.8-2.1,\ 13.8-2.1)=(11.7,\ 15.9)`

Hence, the 95% confidence interval estimate for the average number of years served by all Supreme Court justices is
`11.7<\mu<15.9`