The accompanying table and the data file Dow Jones show percentage changes (xi) in the Dow Jones index over the first five trading days of each of 13 years and also the corresponding percentage changes

(yi) in the index over the whole year.

a. Calculate the sample correlation.

b. Test, at the 10% significance level against a two-sided alternative, the null hypothesis that the population correlation is 0.

x y x y 1.5 14.9 5.6 2.3 0.2 -9.2 -1.4 11.9 -0.1 19.6 1.4 27.0 2.8 20.3 1.5 -4.3 2.2 -3.7 4.7 20.3 -1.6 27.7 1.1 4.2 -1.3 22.6