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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.

User Likern
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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

User Fantasmic
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