Question

A survey was conducted that asked 1016 people how many books they had read in the past year. Results indicated that x = 13.2 books and s = 16.6 books. Construct a 95% confidence interval for the mean number of books people read. Interpret the interval. Click the icon to view the table of critical t-values. 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.) O A. If repeated samples are taken, 95% of them will have a sample mean between and OB. There is a 95% chance that the true mean number of books read is between and OC. There is 95% confidence that the population mean number of books read is between and .

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 13.2

sample standard deviation = s = 16.6

sample size = n = 1016

Degrees of freedom = df = n - 1 = 1016 - 1 = 1015

At 95% confidence level

$\alpha$ = 1 - 95%

$\alpha$ =1 - 0.95 =0.05

$\alpha$/2 = 0.025

t$\alpha$/2,df = t_{0.025, 1015} = 1.962

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 1.962 * ( 16.6 / $\sqrt$ 1016)

Margin of error = E = 1.02

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

$\bar x$  ± E

= 13.2  ± 1.02

=( 12.18, 14.22)

correct option is =C.

There is 95% confidence that the population mean number of books read is between 12.18 and 14.22.