Question

Determine the sample size necessary under the following conditions.

A) To estimate u with o (sigma / standard deviation) = 44, E = 3, 95% confidence

B) To estimate u with a range of values from 20 to 88 with E = 2 and 90% confidence

C) To estimate p with p unknown, E = 0.4, and 98% confidence

D) To estimate p with E = .03, 95% confidence, and p thought to be approximately .70

(Round up your answers to the nearest integer.)

Answer 1

Solution :

A) Z/2 = Z0.025 = 1.96  

sample size = n = [Z/2* / E] 2

n = [1.96 * 44 / 3]2

n = 826.37

Sample size = n = 827

B) Z/2 = Z0.05 = 1.645

standard deviation = = 88 - 20 / 4 = 17

sample size = n = [Z/2* / E] 2

n = [1.645 * 17 / 2 ]2

n = 195.51

Sample size = n = 196

C) =  1 - =   0.5

Z/2 = Z0.01 = 2.33

margin of error = E =0.4

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.33 / 0.4)2 * 0.5 * 0.5

= 8.48

sample size = n = 9

D) = 0.70

1 - = 1 - 0.70 = 0.30

Z/2 = Z0.025 = 1.96

margin of error = E =0.03

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.96 / 0.03)2 * 0.70 * 0.30

= 896.37

sample size = n = 897