Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was​ 6.6, construct a​ 99% confidence interval for the mean score of all students.

A.92.95 <μ <97.05

B.92.03 <μ <97.97

C.91.69 <μ <98.31

D.91.68 <μ <98.32

Answer 1

Solution :

Given that,

t /2,df = 2.756

Margin of error = E = t/2,df * (s /n)

= 2.756 * (6.6 / 30)

Margin of error = E = 3.32

The 99% confidence interval estimate of the population mean is,

- E < < + E

95 - 3.32 < < 95 + 3.32

91.68 < < 98.32

option D. is correct