Question

A poll conducted in

1978

asked

1004

​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 overbarxequals=19.3

books and

sequals=20.3

books.

​(a) Construct a

9999​%

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

1004

people. The results of the survey indicated that

x overbarxequals=12.7

books and

sequals=15.7

books. A

9999​%

confidence interval for this survey is

left parenthesis 11.42 comma 13.98 right parenthesis(11.42, 13.98).

Were people reading more in

1978

than they are​ today?

Answer 1

a)

Degrees of freedom df = n-1 = 1004 -1 = 1003

t critical value at 0.01 significance level for 1003 df = 2.581

99% confidnece interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

19.3 - 2.581 * 20.3 / sqrt(1004) < < 19.3 + 2.581 * 20.3 / sqrt(1004)

17.65 < < 20.95

99% CI is ( 17.65 , 20.95)

Interpretation - The mean number of books read either all or part of during the preceding year

is between 17.65 and 20.95

b)

Confidence interval for today is (11.42 , 13.98)

Comparing this confidence interval with 1978th interval (17.65 , 20.95), it is clear that ,

people reading more in 1978 then they are today.