Question

question 7 of 10
which sample size will produce the widest 95% confidence interval, given a sample proportion of 0.5?
a. 40
b. 70
c. 50
d. 60

Explanation:

Step1: Recall CI width formula for proportion

The width of a 95% confidence interval for a proportion is proportional to $\frac{1}{\sqrt{n}}$, where $n$ is the sample size.

Step2: Relate sample size to width

Smaller $n$ leads to larger $\frac{1}{\sqrt{n}}$, hence wider interval.

Step3: Identify smallest sample size

Among options 40,70,50,60, the smallest is 40.

Answer:

A. 40