With reference to Exercise 65, use the formula obtained in Exercise 31 to construct a 95% confidence interval for ρ.
Exercise 65
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.
Exercise 31
By solving the double inequality 
(with z given by the formula in the previous page) for ρ, derive a (1 - α)100% confidence interval formula for ρ.