Using the formula for the margin of error of a confidence interval of proportions, the sample size that will generate the widest interval is given by:
D. 50
A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A wider interval has a larger margin of error, hence a smaller sample size n is desired, and option D is correct.
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