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 .At the 5% significance level,which of the following is the critical value of the test statistic? A) 2.353 B) 2.571 C) 2.776 D) 3.182

Question

Quizplus · Accepted Answer

The critical value for a two-tailed test with 5% significance level and 5 degrees of freedom (n-2) is 2.571. However, since the alternative hypothesis is two-tailed and we do not know the direction of the correlation, we need to use a t-distribution with n-2 degrees of freedom to find the critical value. With n=5, the critical value is 3.182.

The Following Data for Five Years of the Annual Returns