Question

A researcher wishes to​ estimate, with 90% confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within 33​% of the true 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 42​%

of the respondents said they think Congress is doing a good or excellent job.

​(c) Compare the results from parts​ (a) and​ (b).

​(a) What is the minimum sample size needed assuming that no prior information is​ available?

n=

​(Round up to the nearest whole number as​ needed.)

Answer 1

a.
Given data,
margin of error =33%
Assume, No preliminary estimate is available
sample proportion is 50%
confidence level is 90%
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.645
Sample Proportion = 0.5
ME = 0.33
n = ( 1.645 / 0.33 )^2 * 0.5*0.5
= 6.212 ~ 7          
b.
Given data,
sample proportion = 42%
confidence level =90%
margin of error = 33%
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.645
Sample Proportion = 0.42
ME = 0.33
n = ( 1.645 / 0.33 )^2 * 0.42*0.58
= 6.053 ~ 7          
c.
from part (a),(b) both sample sizes are equal approximately