# 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.)

Question
Study design
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.)

2021-02-09
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:
$$\displaystyle{n}=\hat{{{p}}}\times{\left({1}-\hat{{{p}}}\right)}\times{\left(\frac{{z}}{{E}}\right)}^{{2}}$$
Step 3
Using all values,
$$\displaystyle{n}={0.5}\times{0.5}\times{\left(\frac{{1.645}}{{0.05}}\right)}^{{2}}\approx{271}$$
Minimum sample size is 271

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