Question

# A researcher wishes to​ estimate, with 90​% ​confidence, the population proportion of adults who eat fast...

A researcher wishes to​ estimate, with 90​% ​confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within 5​% 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 38​% of the respondents said they eat fast food four to six times per week. ​(c) Compare the results from parts​ (a) and​ (b).

Given : Margin of error=E=5%=0.05

Significance level=

Now , the critical value is , ; From Z-table

(a) Since , there is no preliminary estimate is available.

Therefore , assume that =0.5

Therefore , the required sample size is ,

(b) Since , the preliminary estimate is available and  =38

Therefore , the required sample size is ,

(c) The sample size is greater in part (a) then the part (b)

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