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% ± 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% ± 4.2%
B)21% ± 3.76%
C)21% ± 3.9%
D)21% ± 4.8%

Question

Quizplus · Accepted Answer

Since the 99% confidence interval is 21% ± 4.5%, we can find the margin of error for a 95% confidence interval by dividing 4.5% by the appropriate value from the t-distribution. Using a calculator or t-table, we find that the appropriate value is approximately 2.576. So the margin of error for a 95% confidence interval would be 4.5% / 2.576 ≈ 1.75%.

Therefore, a 95% confidence interval would be 21% ± 1.75%, which corresponds to answer choices A, B, and C.

Answer choice D, however, gives a margin of error of 4.8%, which is larger than the margin of error for even the 99% confidence interval. Therefore, it could not be a valid 95% confidence interval.

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