Question

A researcher wishes to​ estimate, with 95​% ​confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. Her estimate must be accurate within 4​% 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 38​% of the respondents said their favorite flavor of ice cream is chocolate. ​
(c) Compare the results from parts​ (a) and​ (b).

Answer 1

a) If no preliminary estimate is available, the minimum sample size needed is 601

b) If 38​% of the respondents said their favorite flavor of ice cream is chocolate in a prior survey, then the minimum sample size​ needed is 566

c) As the proportion estimate gets smaller, minimum sample size needed decreases.

Explanation:

The following formula is used to compute the minimum sample size required to estimate the population proportion of adults who say chocolate is their favorite ice cream flavor within the margin of error 4%:

n≥ p×(1-p) ×
`((z)/(ME) )^2` where

• n is the sample size

• p is the proportion of adults who say chocolate is their favorite ice cream flavor

• z is the corresponding z-score for 95% confidence level (1.96)

• ME is the margin of error in the estimation (4% or 0.04)

(a) When p is not known p is assumed 0.5. Then

n≥ 0.5×0.5×
`((1.96)/(0.04) )^2` =600.25

(b) if p=0.38 (38%) then

n≥ 0.38×0.62×
`((1.96)/(0.04) )^2` =565.68