An SRS of 16 Spokane County Schools seniors had a mean SAT v

An SRS of 16 Spokane County Schools\' seniors had a mean SAT verbal score of 500 with a standard deviation of s=100. You know that the population is normally distributed. You wish to determine a 90% confidence interval for the mean SAT verbal score

Solution

(A) The degree of freeom=n-1=16-1=15

Given a=1-0.9=0.1, the critical value is t(0.05, df=15) =1.75 (from student t table)

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(B) So the lower bound is

xbar - t*s/vn =500 -1.75*100/sqrt(16 ) =456.25

So the upper bound is

xbar + t*s/vn =500 +1.75*100/sqrt(16 ) =543.75