One hundred tomato plants were randomly selected from a large garden, and a 90% confidence interval was computed to determine the true proportion of plants that produce useable tomatoes. The interval is 0.86 to 0.92.What would happen to the width of the confidence interval if the sample size was quadrupled?
Answer
A
The width of the interval would quadruple.
B
The width of the interval would double.
C
The interval would be one-fourth the original width.
D
The interval would be half the original width.
Explanation
For a proportion, the confidence interval’s margin of error—and therefore its width—scales approximately as 1/√n. Quadrupling the sample size multiplies the width by 1/√4 = 1/2, so the interval would be half its original width. The correct choice is D.
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