Question

A survey was conducted that asked 1023 people how many books they had read in the past year. Results indicated that x over bar x equals=15.4 books and s equals=18.2

books. Construct a 95​% confidence interval for the mean number of books people read. Interpret the interval.

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.

​(Use ascending order. Round to two decimal places as​ needed.)

A. There is 95​% confidence that the population mean number of books read is between __ and __

B.There is a 95​% chance that the true mean number of books read is between __ and __

C.If repeated samples are​ taken, 95​% of them will have a sample mean between __ and __

.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 15.4

sample standard deviation = s = 18.2

sample size = n = 1023

Degrees of freedom = df = n - 1 = 1022

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,1022 = 1.962

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

= 1.962 * (18.2 / 1023)

= 1.12

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

- E < < + E

15.4 - 1.12 < < 15.4 + 1.12

14.28 < < 16.52

(14.28 , 16.52)

A. There is 95​% confidence that the population mean number of books read is between 14.28 and 16.52