Question

A researcher wishes to​ estimate, with 90​% ​confidence, the population proportion of adults who are confident with their​ country's banking system. His estimate must be accurate within 5​% 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 25​% 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?

Answer 1

Solution :

Given that,

margin of error = E = 5% = 0.05

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

(a)

= 0.5

1 - = 1 - 0.5 = 0.5

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

= (1.645 / 0.05)² * 0.5 * 0.5

= 270.60 = 271

sample size = 271

(b)

= 258% = 0.25

1 - = 1 - 0.25 = 0.75

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

= (1.645 / 0.05)² * 0.25 * 0.75

= 202.95 = 203

sample size = 203

(c)

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