Question

A survey was conducted that asked 1018 people how many books they had read in the past year. Results indicated that x 116 books and s 166 books. Costruct a 90% 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 90% 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 There is a 90% probability that the true mean number of books read is between and B. repeated samples are taken. 90% of them will have a samole mean between and

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 11.6

S = 16.6

n = 1018

df = n – 1 = 1017

Confidence level = 90%

Critical t value = 1.6464

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 11.6 ± 1.6464*16.6/sqrt(1018)

Confidence interval = 11.6 ± 0.8566

Lower limit = 11.6 - 0.8566 = 10.74

Upper limit = 11.6 + 0.8566 =12.46

Confidence interval = (10.74, 12.46)

Answer: B. If repeated samples are taken, 90% of them will have a sample mean between 10.74 and 12.46.