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

33​%

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

3838​%

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 = 33% = 0.33

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

a)

= 0.5

1 - = 1 - 0.5 = 0.5

Sample size = (  Z_/2 / E)² * * (1 - )

= (1.96 / 0.33)² * 0.5 * 0.5

= 8.81 = 9

Sample size = n = 9

b)

= 38% = 0.38

1 - = 1 - 0.38 = 0.62

Sample size = (  Z_/2 / E)² * * (1 - )

= (1.96 / 0.33)² * 0.38 * 0.62

= 8.31 = 9

Sample size = n = 9

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