Question

A researcher wishes to​ estimate, with 95​%

​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 5​% 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

22​%

of the respondents said they think their president can control the price of gasoline.

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

Answer 1

Solution :

Given that,

margin of error = E = 0.05

Z_/2 = 1.96

(a)

= 0.5

1 - = 0.5

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (1.96 / 0.05)² * 0.5 * 0.5

= 385

sample size = n = 385

(b)

= 0.22

1 - = 0.78

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (1.96 / 0.05)² * 0.22 * 0.78

= 264

sample size = n = 264

(c)

Having an estimate of the population proportion reduces the minimum sample size is needed .