Question

A researcher wishes to​ estimate, with 99​% ​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 32​% 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:

a ) Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 4% = 0.04

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

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

= (2.576 / 0.04)² * 0.5 * 0.5

=1036.84

= 1037

n = sample size = 1037

b ) Given that,

= 0.32

1 - = 1 - 0.32 = 0.68

margin of error = E = 4% = 0.04

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

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

= (2.576 / 0.04)² * 0.32 * 0.68

= 902.46

= 902

n = sample size = 902

c ) Parts a ) is more than sample size of parts b )