Question

A researcher wishes to​ estimate, with

ninety percent*

​confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. Her estimate must be accurate within

twenty two percent*

of the population proportion.

Now:

​(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

twenty percent

of the respondents said their favorite flavor of ice cream is chocolate.

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

​

Answer 1

( please check if margin of error is 22% as it seems to be too bigger for proportion interval and revert if it is something else)

a)

here margin of error E =	0.220
for90% CI crtiical Z          =	1.645
estimated proportion=p=	0.5000
required sample size n =	p*(1-p)*(z/E)2=	14.00

b)

here margin of error E =	0.220
for90% CI crtiical Z          =	1.645
estimated proportion=p=	0.2000
required sample size n =	p*(1-p)*(z/E)2=	9.00

c)required sample size is smalller for part b) as prior estimate is known