A researcher wishes to estimate, with 99% confidence, the population proportion

Question

A researcher wishes to estimate, with 99% confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. Her estimate must be accurate within 44% 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 28% of the respondents said their favorite flavor of ice cream is chocolate.

(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.)

Explanation / Answer

a.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.576
Sample Proportion = 0.5
ME = 0.44
n = ( 2.576 / 0.44 )^2 * 0.5*0.5
= 8.569 ~ 9
b.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.576
Sample Proportion = 0.28
ME = 0.44
n = ( 2.576 / 0.44 )^2 * 0.28*0.72
= 6.91 ~ 7
c.
part b has the larger sample size

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