Dr. Cyril conducts a simple random sample of 500 men who became fathers for the first time in the past year. He finds that 23% of them report being unsure of their ability to be good fathers, plus or minus 4%. What does this mean?
A)The true percentage of fathers who feel this way is 23%.
B)If this study was done many times, the estimate of father uncertainty would be 23% about 4% of the time.
C)We can be 4% sure that the estimate of father uncertainty would be 23% of fathers.
D)If the study was done many times, the estimate of father uncertainty would be between 19% and 27%.

Question

Quizplus · Accepted Answer

The statement "plus or minus 4%" means that the margin of error is 4%. Therefore, we can be 95% confident that if the study was done many times, the true percentage of fathers who feel unsure would be between 19% and 27%. Therefore, option D is the best choice. Option A is incorrect because the margin of error suggests that we cannot say with 100% certainty that the true percentage is exactly 23%. Option B is incorrect because it implies that the estimate would always be 23% with a margin of error of 4%, which is not true. Option C is incorrect because it suggests that the margin of error provides some sort of certainty about the estimate, which is not true either.

Dr Cyril Conducts a Simple Random Sample of 500 Men