Question

A poll conducted in 1974 asked 1007 ?people, "During the past? year, about how many? books, either hardcover or? paperback, did you read either all or part of the way? through?" Results of the survey indicated that x=18.8 books and s=19.8 books.

?(a) Construct a 99?% confidence interval for the mean number of books read either all or part of during the preceding year. Interpret the interval.

?(b) Compare these results to a recentrecent survey of 1007 people. The results of the survey indicated that x =13.5 books and s=16.8 books. A 99?% confidence interval for this survey is (12.46,14.54) Were people reading more in 1974 than they are? today?

(a) The 99?% confidence interval for 1974 is: (__,__)

Interpret the confidence interval. Which of the following is? correct?

a) We are 99?% confident that the mean number of books read in 1974 is in the interval.

b) We are 99?% confident that the mean number of books read in 1974 is not in the interval.

c) The probability that the interval does not contain the mean number of books read is 99%.

d) The probability that the interval contains the mean number of books read is 99 %.

?(B) Were people reading more in 1974 than tyhey are today

a) No, people were reading less in 1974 than they are reading today

b) People were reading approximately the same number of books in 1974 as they are today

c) Yes, people were reading more in 1974 than they are reading today.

Answer 1

Solution:-

A) 99?% confidence interval for the mean number of books read either all or part of during the preceding year. Interpret the interval is C.I = (17.193, 20.407).

C.I = 18.8 + 2.576 × 0.62395

C.I = 18.8 + 1.6073

C.I = (17.193, 20.407)

We are 99?% confident that the mean number of books read in 1974 is in the interval (17.193, 20.407).

B) c) Yes, people were reading more in 1974 than they are reading today. Since the lower limit and upper limit of 99?% confident that the mean number of books read in 1974 is greater than the upper limit of 99?% confidence interval for the recent survey.