Answer:
The most conservative sample size is 2401.
Step-by-step explanation:
We are given the following in the question:
We are not given any approximation of s]ample proportion, thus,
[tex]\hat{p} = 0.5[/tex]
We have to construct a 95% confidence interval.
Margin of error = 2% = 0.02
Formula for margin of error =
[tex]z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
Putting values, we get,
[tex]0.02 = 1.96\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\0.02 = 1.96\times \sqrt{\dfrac{0.5(1-0.5)}{n}}\\\\\sqrt{n} = 1.96\times \dfrac{\sqrt{0.5(1-0.5)}}{0.02}\\\\\sqrt{n}=49\\n = 2401[/tex]
Thus, the most conservative sample size is 2401.
