Question

A survey was conducted that had asked 1068 people how many books they had read in the past year. Results indicated that X=13.3 books and S=18.1 books. Construct a 96% confidence interval for the mean number of books people read. Interpret the interval.

Construct a 96% 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 96% confidence that the population mean number of books read is between __ and __.

B. There is a 96% chance that the true mean number of books read is between __ and ___.

C. If repeated samples are taken, 96% of them will have a sample mean between ___ and ____.

Answer 1

The formula for estimation of confidence interval is:

μ = X ± Z(s_M)

where:

X= sample mean=13.3
Z = Z statistic determined by confidence level=2.06 at 96 % Confidence level
s_x = standard error = √(s²/n)

X= 13.3
Z= 2.06
s_x = √(18.1²/1068) = 0.55

Hence

μ = 13.3 ± 2.06*0.55

μ = 13.3 ± 1.133

Interpretation:

A. There is a 96% confidence that the population mean number of books read is between _12.167_ and _14.433_.

Z score is calculated using Z statistic table below