A researcher wishes to​ estimate, with 90​% ​confidence, the population proportion of adults who support labeling legislation for genetically modified organisms​ (GMOs).

Her estimate must be accurate within 6​% of the true 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 84​% of the respondents said they support labeling legislation for GMOs.

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