Question

A researcher wishes to? estimate, with 90?% ?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.) ?(?b) What is the minimum sample size needed using a prior study that found that 18?% of the respondents said their favorite ice cream flavor is? chocolate? nequals nothing ?(Round up to the nearest whole number as? needed.) ?(c) How do the results from? (a) and? (b) compare? A. Having an estimate of the population proportion reduces the minimum sample size needed. B. Having an estimate of the population proportion raises the minimum sample size needed. C. Having an estimate of the population proportion has no effect on the minimum sample size needed.

Answer 1

a) No proportion estimate given so we will assume:

p = q = 0.5

E = 0.02

For 90% confidence, z = 1.645

Hence,

Sample size

n = 1692

b) p = 0.18, q = 0.82

E = 0.02

For 90% confidence, z = 1.645

Hence,

Sample size

n = 999

c) Option A is correct.