Question

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 2​% 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 38​% 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

As per the provided information:

Margin of error (M.E.) is 0.02 (or 2%)

Confidence level (c) is 0.99.

For the confidence level 0.99, the two tailed critical value obtained from the z table is +/- 2.58.

a). No preliminary estimate is provided, so we assume p = 0.5.

The minimum sample size (n) can be calculated as:

Therefore, the required sample size is 4160.

b).

As per the prior study, the estimated proportion of respondents said they think their president can control the price of gasoline, = 0.38 or 38%.

The minimum sample size (n) can be calculated as:

Therefore, the required sample size is 3921.

c).

On comparing the results of part a) and part b), the required sample size in case of known estimated proportion is small as compared to unknown preliminary estimate.