 # 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 0.05? (Round your answer up to the nearest whole number.) tabita57i 2020-12-24 Answered
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 0.05? (Round your answer up to the nearest whole number.)
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Step 1
The confidence level is 95%
Therefore, $\alpha =0.05\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\frac{\alpha }{2}=0.025$.
The margin of error is .05
Since the proportion is not known, p= 0.5 and 1–p= 0.5.
Thus, ${z}_{\frac{\alpha }{2}}=1.96$ (using the formula =NORM.INV (0.975, 0,1)).
Step 2
Then the sample size can be obtained as follows:
$n=p\left(1-p\right){\left(\frac{z}{E}\right)}^{2}$
$=0.5×\left(1-0.5\right)×{\left(\frac{1.96}{0.05}\right)}^{2}$
=384.16
=385
Thus, the sample size is 385.
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