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

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

18​%

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?

nequals=nothing

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

Answer 1

Solution :

Given that,

margin of error = E = 0.02

Z_/2 = 2.576

(a)

= 0.5

1 - = 0.5

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

= (2.576 / 0.02)² * 0.5 * 0.5  

= 4148

sample size = n = 4148

b)

= 0.18

1 - = 0.82

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

= (2.576 / 0.02)² * 0.18 * 0.82

= 2449

sample size = n = 2449

C)

Having an estimate of the population proportion reduces the minimum sample size is needed .