Question

A researcher wishes to​ estimate, with 95​% ​confidence, the population proportion of adults who are confident with their​ country's banking system. His estimate must be accurate within 4​% of the population proportion. ​(a) No preliminary estimate is available. Find the minimum sample size needed. ​(b) Find the minimum sample size​ needed, using a prior study that found that 34​% of the respondents said they are confident with their​ country's banking system. ​(c) Compare the results from parts ​(a) and ​(b). ​(a) What is the minimum sample size needed assuming that no prior information is​ available? nequals nothing ​(Round up to the nearest whole number as​ needed.)

Answer 1

Solution :

Given that,

margin of error = E = 0.04

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

(a)

= 0.5

1 - = 1 - 0.5 = 0.5

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

= (1.96 / 0.04)² * 0.5 * 0.5

= 600.25

sample size = 600

(b)

= 0.34

1 - = 1 - 0.34 = 0.66

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

= (1.96 / 0.04)² * 0.34 * 0.66

= 538.78 = 539

sample size = 539

(c)

Having an estimate of the population proportion reduces the minimum sample size is needed .