Question

A survey was conducted that asked 1045 people how many books they had read in the past year. Results indicated that x overbarxequals=14.1 books and sequals=16.4 books. Construct a 96​% confidence interval for the mean number of books people read. Interpret the interval.

Answer 1

Solution :

Given that,

= 14.1

s = = 16.4

n = 1045

At 96% confidence level the z is ,

  = 1 - 96% = 1 - 0.96 = 0.04

/ 2 = 0.04 / 2 = 0.02

Z_/2 = Z_0.02 =2.054

Margin of error = E = Z_/2* ( /n)

= 2.054 * ( 16.4/ 1045)

= 1.0420

At 96% confidence interval estimate of the population mean is,

- E < < + E

14.1 - 1.0420 < < 14.1 + 1.0420

13.0580 < < 15.1420

(13.0580 ,  15.1420 )