An achievement test is said to be reliable if a student who takes the test several times will consistently get high (or low) scores. One way of checking the reliability of a test is to divide it into two parts, usually the even-numbered problems and the odd- numbered problems, and observe the correlation between the scores that students get in both halves of the test. Thus, the following data represent the grades, x and y, that 20 students obtained for the even- numbered problems and the odd- numbered problems of a new objective test designed to test eighth grade achievement in general science:

Calculate r for these data and test its significance, that is, the null hypothesis ρ = 0 against the alternative hypothesis ρ ‰  0 at the 0.05 level of significance.

y-42 31 38 22 34 37 38 35 32 43 332 3 3 3 3 3 4 3984327349 3332333333 9497539078 2718407 2343243432