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 2 ?% 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 36 ?% of the respondents said they are confident with their? country's banking system. ?(c) Compare the results from parts ?(a) and ?(b).

Answer 1

Solution :

Given that,

Margin of error = E = 2% = 0.02

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

(a)

Sample size = (  Z_/2 / E)² * * (1 - )

= (2.576 / 0.02)² * 0.5 * 0.5

= 4147.36 = 4148

Sample size = n = 4148

(b) = 36% = 0.36

1 - = 1 - 0.36 = 0.64

Sample size = (  Z_/2 / E)² * * (1 - )

= (2.576 / 0.02)² * 0.36 * 0.64

= 3822.20 = 3823

Sample size = n = 3823

C) The sample proportion is smaller then sample size is decreases .