# When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 90% confident that the population proportion is estimated to within 0.05? (Round your answer up to the nearest whole number.)

When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 90% confident that the population proportion is estimated to within 0.05? (Round your answer up to the nearest whole number.)
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Nichole Watt
Step 1
Given:
Confidence level = 0.90
Z for 90% confidence level = 1.645 …using z-table
Margin of error = E = 0.05
Step 2
Proportion of women = 0.5 …As it is not given, it can be assumed to be 0.5
We have to find minimum sample size.
Formula:
$n=\stackrel{^}{p}×\left(1-\stackrel{^}{p}\right)×{\left(\frac{z}{E}\right)}^{2}$
Step 3
Using all values,
$n=0.5×0.5×{\left(\frac{1.645}{0.05}\right)}^{2}\approx 271$
Minimum sample size is 271
Jeffrey Jordon