The National Assessment of Educational Progress NAEP include

The National Assessment of Educational Progress (NAEP) includes a mathematics test for high school seniors. Scores on the test range from 0 to 300. Suppose that you give the NAEP test to an SRS of 900 12th-graders from a large population in which the scores have mean = 150 and standard deviation = 35. The mean x will vary if you take repeated samples. Suppose that we computed a 99% confidence interval for .

A. This 99% confidence interval would have a smaller margin of error than the 95% confidence interval. B. This 99% confidence interval would have a larger margin of error than the 95% confidence interval. C. This 99% confidence interval could have either a smaller or a larger margin of error than the 95% confidence interval. This varies from sample to sample.

Solution

Margin of error is inversely associated with the sample size, that is when the sample size increases the margin of error decreases and vice versa. Thus, the required answer is C. This 99% confidence interval could have either a smaller or a larger margin of error than the 95% confidence interval. This varies from sample to sample.