A researcher wishes to​ estimate, with 99​% ​confidence, the population proportion of adults who say chocolate ...

A researcher wishes to​ estimate, with 99​% ​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) What is the minimum sample size needed assuming that no prior information is​ available?

​(b) Find the minimum sample size​ needed, using a prior study that found that 20​% of the respondents said their favorite flavor of ice cream is chocolate.

​(c) Compare the results from parts​ (a) and​ (b).