Question

A survey was conducted that asked

977977

people how many books they had read in the past year. Results indicated that

x overbarxequals=13.713.7

books and

sequals=18.718.7

books. Construct a

9090​%

confidence interval for the mean number of books people read. Interpret the interval.

Construct a

90​%

confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice.

Answer 1

sample mean, xbar = 13.7
sample standard deviation, s = 18.7
sample size, n = 977
degrees of freedom, df = n - 1 = 976

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.646

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (13.7 - 1.646 * 18.7/sqrt(977) , 13.7 + 1.646 * 18.7/sqrt(977))
CI = (12.72 , 14.68)