Question

A sample of n = 168 students was asked, "Do you believe in love at first sight?" The choices below show confidence intervals, in scrambled order, for 90%, 95%, 98%, and 99% confidence levels for the population proportion who would answer yes. Which choice gives the 99% confidence interval? Group of answer choices

Answer 1

Group of answer choices:

A) 0.56 to 0.68

B) 0.52 to 0.72

C) 0.53 to 0.71

D) 0.55 to 0.69

Answer:

Option B) 0.52 to 0.72

Explanation:

This is a very trivial exercise. A very good point that is required to solve this question is that the wider the Confidence level, the wider the Confidence Interval.

Let us consider the options one after the other for the width of interval:

Option A) 0.56 to 0.68

Width of Interval = 0.68 - 0.56 = 0.12

Option B) 0.52 to 0.72

Width of Interval = 0.72 - 0.52 = 0.20

Option C) 0.53 to 0.71

Width of Interval = 0.71 - 0.53 = 0.18

Option D) 0.55 to 0.69

Width of Interval = 0.69 - 0.55 = 0.14

Assigning the confidence level based on the width of the confidence intervals:

Option A) 0.56 to 0.68 = 90%

Option D) 0.55 to 0.69 = 95%

Option C) 0.53 to 0.71 = 98%

Option B) 0.52 to 0.72 = 99%