Question

A recent Gallup poll asked 1006 Americans, "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 X̄ = 13.4 books and s = 16.6 books. Construct a 99% CI for the mean number of books, that Americans read either all or part of during the preceding year. Interpret the interval.

Answer 1

Solution :

sample size = n = 1006

Degrees of freedom = df = n - 1 = 1005

t _/2,df = 2.581

Margin of error = E = t_/2,df * (s /n)

= 2.581 * (16.6 / 1006)

Margin of error = E = 1.35

The 99% confidence interval estimate of the population mean is,

- E < < + E

13.4 - 1.35 < < 13.4 + 1.35

12.05 < < 14.75

(12.05 , 14.75)