Question

survey was conducted that asked 1026 people how many books they had read in the past year. Results indicated that x overbar equals14.3 books and s equals 15.6 books. Construct a 96​% confidence interval for the mean number of books people read. Interpret the interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 14.3

sample standard deviation = s = 15.6

sample size = n = 1026

Degrees of freedom = df = n - 1 = 1025

At 99% confidence level the z is ,

= 1 - 96% = 1 - 0.96= 0.04

/ 2 = 0.04 / 2 = 0.02

t _/2,df = t_0.02,1025 = 2.056

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

= 2.056 * (15.6 / 1026)

= 1.001

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

- E < < + E

14.3 - 1.001 < < 14.3 + 1.001

13.299 < < 15.301

Therefore, 96% confidence interval mean number of people of books read in the past year in between 13.299 to 15.301.