## A researcher wishes to estimate, with 95% confidence, the population proportion of adults who say chocolate is their favorite ice cream f

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).

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2021-10-12T13:17:59+00:00
2021-10-12T13:17:59+00:00 1 Answer
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## Answers ( )

Answer: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.

Step-by-step 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) × where

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

n≥ 0.5×0.5× =600.25

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

n≥ 0.38×0.62× =565.68