A researcher wishes to estimate, with 90% confidence, the population proportion

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 46% 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? (Round up to the nearest whole number as needed.)

Explanation / Answer

here margin of error E =0.02

and for 90% CI, z=1.6449

also for no prior estimate p=0.5

a) sample size =p(!-p)(z/E)2 =1691

b) for p =0.46 ; sample size =1681

c) for no prior estimate we require larger sample size.

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