The following data for five years of the annual returns for two of Vanguard's mutual funds, the Vanguard Energy Fund (x) and the Vanguard Healthcare Fund (y), were given as s_x= 35.77, s_y= 13.34, s_xy= 447.68. The competing hypotheses are H₀: ρ_xy = 0, H_A: ρ_xy ≠ 0. Which of the following is the value of the test statistic? A) 7.47 B) 5.74 C) 4.77 D) 4.27

Question

Quizplus · Accepted Answer

We can use the formula for the test statistic of a hypothesis test for the correlation coefficient:

t = (r - 0) / (sqrt((1-r^2)/(n-2)))

Where r is the sample correlation coefficient, 0 is the null hypothesis value, and n is the sample size.

Plugging in the given values, we get:

t = (447.68 - 0) / (sqrt((1-(447.68^2))/(5-2))) = 4.77

Therefore, the test statistic is 4.77, which corresponds to choice C.

The Following Data for Five Years of the Annual Returns