or A researcher wares to estimate, with 90% confidence·the population proportion

Question

or A researcher wares to estimate, with 90% confidence·the population proportion of adults who say chocolate is ter tevoríte oe creen favor. Her estimate must be accurate within 4% ofthe ulation proportion. (a) No preiminary estimate is available. Find the minimum sample size needed (b) Find the minimum sample sze needed, using a prior study that found hat 22% ofthe respondents said ter favorie ta or 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? nRound up to the nearest whole number as needed.) (b) What is the mininum sample size needed using a prior study that found that 22% of the respondents said their favorite ice cream flavor is chocolate? nRound up to the nearest whole number as needed) (c) How do the resuilts from (a) and (b) compare? O A. Having an estimate of the population proportion raises the minimum sample size needed OB.Having an estimate of the population proportion has no efect on the minimum sample size needed ° C. Having an estimate of the population proportion reduces he mnimum sample size needed.

Explanation / Answer

a)

We are given that

Z critical value = 1.645 at 90% confidence

Margin error = 0.04

If there is no preliminary information then proportion will be 50%

i.e P = Q = 0.5

Now

Sample size(n)

= (z critical value / 0.02)2 PQ

= (1.645 / 0.04)2 0.5*0.5

= 422.82

Approximately sample size will be 423

b) given that P = 0.22

and Q = 1 - 0.22 = 0.78

Sample size(n)

= (z critical value / 0.04)2 PQ

= (1.645 / 0.04)2 0.22*0.78

= 290.22

Approximately sample size will be 291

c) Option C is correct

since 291 < 423

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