16.32 The following table gives the recorded grades for 10 students on a midterm test and the final examination in a calculus course:

Midterm Final Student Test Examination L.S.A.

W.P.B.

R.W.K.

J.R.L.

J.K.L.

D.L.P.

B.L.P.

D.W.M.

M.N.M.

R.H.S.

84 98 91 72 86 93 80 0

92 87 73 63 87 66 78 78 91 0

88 77

(a) Calculate the rank correlation coefficient.

(b) Test the null hypothesis that ρ = 0 against the alternative that ρ > 0. Use α = 0.025.