Question

A survey was conducted that asked 954 people how many books they had read in the past year. Results indicated that x overbarequals15.3 books and sequals18.8 books. Construct a 95​% confidence interval for the mean number of books people read. Interpret the interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 15.3

sample standard deviation = s = 18.1

sample size = n = 954

Degrees of freedom = df = n - 1 = 954 -1 = 953

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,953 = 1.962

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

= 1.962 * ( 18.1/ 954)

= 1.1

The 95% confidence interval estimate of the population mean is,

- E < < + E

15.3 - 1.1 < < 15.3 + 1.1

14.2 < < 16.4

(14.2 , 16.4)