Using the z-distribution, the sample size that will produce the widest confidence interval is given by:
D. 36.
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]
The widest interval has the highest margin of error, and since the margin of error is inversely proportional to the sample size, a lower sample size generates a higher margin of error, hence option D is correct.
More can be learned about the z-distribution at https://brainly.com/question/25890103
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