When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.02? (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 95% confident that the population proportion is estimated to within 0.02? (Round your answer up to the nearest whole number.)

Question
Study design
asked 2020-11-05
When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.02? (Round your answer up to the nearest whole number.)

Answers (1)

2020-11-06
Step 1
Solution:
From the given information, confidence level is 0.95 and E=0.02.
\(\displaystyle{1}-\alpha={0.95}\)
\(\displaystyle\alpha={1}-{0.95}\)
\(\displaystyle\alpha={0.05}\)
Step 2
Since the proportion is not given 0.5 should be taken.
Then,
\(\displaystyle{n}={\left(\frac{{Z}_{{\frac{\alpha}{{2}}}}}{{E}}\right)}^{{2}}{p}{\left({1}-{p}\right)}\)
\(\displaystyle={\left(\frac{{Z}_{{\frac{{0.05}}{{2}}}}}{{0.02}}\right)}^{{2}}{0.5}{\left({1}-{0.5}\right)}\)
\(\displaystyle={\left(\frac{{Z}_{{0.025}}}{{0.02}}\right)}^{{2}}{0.25}\)
\(\displaystyle={\left(\frac{{1.96}}{{0.02}}\right)}^{{2}}{0.25}{\left[{U}{\sin{{g}}}{e}{x}{c}{e}{l}{f}{u}{n}{c}{t}{i}{o}{n}={N}{O}{R}{M}.{I}{N}{V}{\left({0.025},{0},{1}\right)}\right]}\)
=2401
Thus. the required number of drivers is 2401.
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