True or False: The width of a confidence interval estimate for a proportion will be
A)narrower for 99% confidence than for 95% confidence.
B)wider for a sample size of 100 than for a sample size of 50.
C)narrower for 90% confidence than for 95% confidence.
D)narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.

Question

Quizplus · Accepted Answer

As the level of confidence increases, the width of the confidence interval increases. Similarly, as the sample size increases, the width of the confidence interval decreases. However, the sample proportion does not have a consistent effect on the width of the confidence interval. Therefore, option A and D are false. Option B is also false as wider confidence intervals are expected with smaller sample sizes. Option C is true as a 90% confidence interval is narrower than a 95% confidence interval. The width of a confidence interval estimate for a proportion is based on the level of confidence, sample size, and sample proportion. The higher the level of confidence, the wider the interval will be, so A is false. The larger the sample size, the narrower the interval will be, so B is false. When the sample proportion is 0.50, the interval will be wider compared to when the sample proportion is closer to 0 or 1, so D is false. Therefore, the only true statement is C, where a lower level of confidence will result in a narrower confidence interval.

True or False: the Width of a Confidence Interval Estimate