(a) What is the minimum sample size needed assuming that no prior information is​ available?   n= ______ ​(Round up to the nearest whole number as​ needed.)     ​(b) What is the minimum sample size needed using a prior study that found that 26​% of the  respondents said they think their president can control the price of​ gasoline?   n= ______ ​(Round up to the nearest whole number as​ needed.)

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A researcher wishes to​ estimate, with 99​% ​confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 4​% 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 26​% of the  respondents said they think their president can control the price of gasoline.

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

 

​(a) What is the minimum sample size needed assuming that no prior information is​ available?

 

n= ______

​(Round up to the nearest whole number as​ needed.)

 

 

​(b) What is the minimum sample size needed using a prior study that found that 26​% of the  respondents said they think their president can control the price of​ gasoline?

 

n= ______

​(Round up to the nearest whole number as​ needed.)

 

Expert Solution
Part a)

Margin of error = 0.04

z-critical value at alpha(0.01) = 2.576

 

The sample size is given by

n = (\frac{z_{0.01} \times 0.5}{ME})^2

n = (\frac{2.576 \times 0.5}{0.04})^2

{\color{Red} n = 1036.84 \approx 1037}

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