Question

1. a What is the size of the smallest sample required to estimate an unknown proportion of customers who would pay for an additional service, to within a maximum error of 0.06 with at least 95% confidence?   1b With reference to the previous problem, how would the required sample size be affected if it is known that the proportion to be estimated is at least 0.75?

Answer 1

Solution :

Given that,

= 0.5

1 - =0.5

margin of error = E = = 0.06

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

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

= (1.96 / 0.06)2 * 0.5 * 0.5

= 266.77

Sample size =267

B

Solution :

Given that,

= 0.75

1 - = 1 - 0.75 = 0.25

margin of error = E = 0.06

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

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

= (1.96 / 0.06)2 * 0.75 * 0.25

= 200.08

Sample size =200