Question

1. Suppose we are interested in how well people do on a standardized test when they take it for a second time. In a random sample of 400 students who took the test for a second time, students gained an average of X-bar = 12 points. Let’s say that the sample comes from a population with σ = 42. The 95% confidence interval for μ (the mean point gain) is:

μ = 12 ± (1.96) (42/√400) = 12 ± 4.12 = 7.88 to 16.12

1. Find the 90% confidence interval for μ (the mean point gain). (1 point)

2. Compare the margin of error for the 95% confidence interval and the 90% confidence interval. How does decreasing the confidence level from 95% to 90% change the margin of error when the sampe size and population standard deviation (σ) stay the same?      (1 point)

3. In the 95% confidence interval, what would happen if the sample size was just 100 students? In other words, how does decreasing the sample size change the margin of error when the confidence level and population standard deviation (σ) stay the same? (1 point)

Answer 1