Question

30) A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of 5 examinations is selected at random and scored. The scores are shown below.

Grade

76

67

76

81

95

A. Compute the standard deviation. (Round to 2 decimal places)

B. At 95% confidence, determine an interval for the mean of the population.

Answer 1

Solution-A:

sample standard deviation=s=10.27132

Solution-b:

df=n-1=5-1=4

alpha=0.05

alpha/2=0.05/2=0.025

t critical in excel==T.INV(0.025,4)=2.77645

xbar=79

s=10.27132

95% confidence interval for mean

xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)

79-2.77645*10.27132/sqrt(5),79+2.77645*10.27132/sqrt(5)

66.24645,91.75355

66.24645<mu<91.75355

95% lower limit=66.24645

95% upper limit=91.75355