Question

A survey was conducted that asked 1014 people how many books they had read in the past year. Results indicated that x overbarequals14.7 books and sequals16.6 books. Construct a 95​% confidence interval for the mean number of books people read. Interpret the interval. LOADING... 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.) A. There is a 95​% chance that the true mean number of books read is between nothing and nothing. B. There is 95​% confidence that the population mean number of books read is between nothing and nothing. C. If repeated samples are​ taken, 95​% of them will have a sample mean between nothing and nothing.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 14.7

sample standard deviation = s = 16.6

sample size = n = 1014

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

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

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

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

= 1.962 * (16.6 / 1014)

= 1.02

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

- E < < + E

14.7 - 1.02 < < 14.7 + 1.02

13.68 < < 15.72

(13.68 , 15.72)

B. There is 95​% confidence that the population mean number of books read is between 13.68 and 15.72 .