Paired versus independent samples: Each student draws two lines, by eye, on a piece of paper. Students should try to make the first line as close to 3 inches long as possible, and the second line as close to 6 inches long as possible. Then students measure the lengths of the lines and calculate the errors between the true lengths and the attempted lengths. Each student reports the error in the 3-inch line, the error in the 6-inch line, and the difference between the errors. Test the hypothesis that the mean error is greater for the 6-inch line with a paired test. Then, pretending the samples are independent, test the same hypothesis using an independent samples test. For which test is the P-value smaller?

Why?