Question

People were polled on how many books the read the previous year. Initial survey results indicate that s=11.6 books.

(a) How many subjects are needed to estimate the mean number of books read the previous year within four books with 95% ​confidence?

(b) How many subjects are needed to estimate the mean number of books read the previous year within two books with 95​% confidence?

(c) How many subjects are needed to estimate the mean number of books read the previous year within four books with 99​% ​confidence?

Answer 1

Solution :

Given that,

Population standard deviation = = 11.6 books.

a) Margin of error = E = 4 books.

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = Z _0.025 = 1.96

sample size = n = [Z_/2* / E] ²

n = [ 1.96 * 11.6 / 4 ]²

n = 32.30

Sample size = n = 33 subjects.

b) Margin of error = E = 2 books.

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [ 1.96 * 11.6 / 2 ]²

n = 129.23

Sample size = n = 130 subjects.

c) Margin of error = 4 books.

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z_/2 = Z _0.005 = 2.576

sample size = n = [Z_/2* / E] ²

n = [ 2.576 * 11.6 / 4 ]²

n = 55.80

Sample size = n = 56 subjects.