Question

A survey was conducted that asked 1014 people how many books they had read in the past year. Results indicated that x over bar x equals=13.6 books and s equals=16.6 books. Construct a 95​% confidence interval for the mean number of books people read. Interpret the interval. Construct a 95​% 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 = = 13.6

sample standard deviation = s = 16.6

sample size = n = 1014

Degrees of freedom = df = n - 1 = 1014 - 1 = 1013

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t_0.025,1013 = 1.962

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

= 1.962 * ( 16.6 / 1014)

Margin of error = E = 1.02

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

  ± E

= 13.6  ± 1.02

= ( 12.58, 14.62 )

A.There is 95​% confidence that the population mean number of books read is between 12.58 and 14.62.