A government report gives a 99% confidence interval for the proportion of welfare recipients who have been receiving welfare benefits for more than 5 years to be 21% $\pm$ 4.5%.Which of the following intervals could not be a 95% confidence interval for the proportion of welfare recipients who have been receiving welfare benefits for more than 5 years?
A)21% $\pm$ 4.2%
B)21% $\pm$ 3.76%
C)21% $\pm$ 3.9%
D)21% $\pm$ 4.8%

Question

A government report gives a 99% confidence interval for the proportion of welfare recipients who have been receiving welfare benefits for more than 5 years to be 21%  $\pm$ 4.5%.Which of the following intervals could not be a 95% confidence interval for the proportion of welfare recipients who have been receiving welfare benefits for more than 5 years?
A)21%  $\pm$ 4.2%
B)21%  $\pm$ 3.76%
C)21%  $\pm$ 3.9%
D)21%  $\pm$ 4.8%

Quizplus · Accepted Answer

Since the given confidence interval is at 99% confidence level, any interval with a narrower width cannot be a 95% confidence interval. Only option D has an interval with wider width than the given interval, so it could be a 95% confidence interval. Options A, B, and C all have narrower intervals, so they cannot be 95% confidence intervals.

A Government Report Gives a 99% Confidence Interval for the Proportion