Question

An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 3% of the true proportion with 97% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy?

Answer 1

Answer:

Minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy is 1309.

Step-by-step explanation:

Consider the provided information.

The estimate accurate to within 3%

Therefore, e = 0.03

The true proportion with 97% confidence.

For 97% CI critical Z = 2.1701

p = 1/2 = 0.5

We can calculate the sample size  by using the formula.

$n = p(1-p)(\frac{z_{\frac{\alpha}{2}}}{e})^2$

Substitute the respective values

$n =0.5(0.5)(\frac{2.1701}{0.03})^2$

$n =0.25(5232.59)$

$n =1308.15$

Hence, minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy is 1309.