Question

The National Assessment of Educational Progress (NAEP) includes a mathematical test for eighth-grade students. Scores on the test range from 0 to 500. Suppose that you give the NAEP test to a simple random sample of 900 eighth-graders from a large population in which the scores have mean m = 285 and standard deviation s = 125. The mean will vary if you take repeated samples.

2. (2 points) The sampling distribution of   is approximately Normal. It has mean m = 285. What is its standard error? Select the best option.

(a) 125

(b) 4.167

(c) 0.139

3. (2 points) Suppose that a simple random sample of 900 eighth- graders has  = 288. Based on this sample, a 95% confidence interval for m is… Select the best option.

(a) 8.17 ± 0.27

(b) 288 ± 8.17

(c) 285 ± 8.17

4. (2 points) In Exercise 2, suppose that we computed a 99% confidence interval for m. Select the best option.

(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.

5. (2 points) Suppose that we took a simple random of 1600 eighth-graders and found  = 288. Compared with a simple random of 900 eighth-graders, the margin of error for a 95% confidence interval for m is

(a) smaller

(b) larger

(c) either smaller or larger but we can’t say which

Answer 1

as we increase the sample size, the margin of error is also get increased.