Question

People in a public library were polled on how many books they read in the last five years. Preliminary survey results indicate the sample standard deviation is 18.61 books. How many subjects are needed to estimate the mean number of books read by library users in the last five years within four books with 99% confidence

Answer 1

144

Explanation:

From information available

Margin of error = 4

S = 18.61

ME = Z-alpha/2 x s/√n

Alpha = 1-0.99

= 0.01

Alpha/2 = 0.01/2

= 0.005

Z-alpha/2 =2.576

Putting into the formula we have

4/1 = 2.576 x 18.61/√n

When we cross multiply

We have

√n = (2.576 x 18.61)/4

√n = 11.98484

n = 11.98484²

n = 143.63

n = 144

144 subjects are needed to do this estimation