Question

a researcher wishes to estimate, with 99% confidence, the population proportion of motor vehicle fatalities that were caused by alcohol - impaired driving. his estimate must be accurate within 4% 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 28% of motor vehicle fatalities that were caused by alcohol - impaired driving.
(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 = 1037 (round up to the nearest whole number as needed.)
(b) what is the minimum sample size needed using a prior study that found that 28% of motor vehicle fatalities that were caused by alcohol - impaired driving?
n = 837 (round up to the nearest whole number as needed.)
(c) how do the results from (a) and (b) compare?
○ a. having an estimate of the population proportion reduces the minimum sample size needed.
○ b. having an estimate of the population proportion raises the minimum sample size needed.
○ c. having an estimate of the population proportion has no effect on the minimum sample size needed.

Explanation:

Step1: Analyze the sample sizes

In part (a), the sample size \(n = 1037\) (no prior estimate). In part (b), the sample size \(n=837\) (with a prior estimate of \(p = 0.28\)).

Step2: Compare the two sample sizes

Since \(837<1037\), having a prior estimate (of the population proportion) reduces the minimum sample size needed.

Answer:

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