Question

People were polled on how many books they read the previous year. Initial survey results indicate that s equals 17.4 books. Complete parts ​(a) through ​(d) below.

a. How many subjects are needed to estimate the mean number of books read the previous year with 90​% ​confidence?

this 90% confidence requires ___ subjects?

b. How many subjects are needed to estimate the mean number of books read the previous year within three books with 90% confidence?

this 90% confidence requires ___ subjects?

c. How many subjects are needed to estimate the mean number of books read the previous year within six books with 99% confidence?

this 99% confidence requires ___ subjects?

Answer 1

Solution :

Given that,

s = 17.4

(a)

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = 1

sample size = n = (Z_/2* s / E) ²

n = (1.645 * 17.4 / 1)²

n = 819.27

n = 820

this 90% confidence requires 820 subjects .

(b)

Margin of error = E = 3

sample size = n = (Z_/2* s / E) ²

n = (1.645 * 17.4 / 3)²

n = 91.03

n = 92

this 90% confidence requires 92 subjects .

(c)

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = 6

sample size = n = (Z_/2* s / E) ²

n = (2.576 * 17.4 / 6)²

n = 55.8

n = 56

this 99% confidence requires 56 subjects .