Question

A survey was conducted that asked 1016 people how many books they had read in the past year. Results indicated that x overbarx =15.6 books and s =17.7 books. Construct a 98​% confidence interval for the mean number of books people read. Interpret the interval.

Construct a 98​% 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 98​% confidence that the population mean number of books read is between _____ and _____

B.There is a 98​% probability that the true mean number of books read is between _____ and ______

C.If repeated samples are​ taken, 98​% of them will have a sample mean between _____ and _____

Let me know if this is possible to do in Statcrunch and if so, how to do it with answers. Thanks!

Answer 1

a) For n - 1= 1015 degrees of freedom, we have from the t distribution tables here:
P( t₁₀₁₅ < 2.33) = 0.99

Therefore, due to symmetry, we have here:
P( -2.33 < t₁₀₁₅ < 2.33) = 0.98

Therefore the 98% confidence interval for the mean number of books people read is obtained here as:

We are 98% confident that the true population mean number of books read is between 14.31 and 16.89. Therefore A is the correct answer here.