Question

Need in the next hour.

The following table shows the annual retums for two of Vanguard's mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund. Use Table 2 Annual Total Returns (in percent) Year 2004 2005 2006 2007 2008 Energy x 31.40 20.20 18.25 34.00 -34.15 Healthcare y 9.45 14.26 9.72 4.42 -17.42 x13.94 27.74 -4.09 Sy 12.52 Sxy 305.64 SOURCE: www.finance.yahoo.com. Calculate and interpret the sample correlation coefficient rxy (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) a. Sample correlation coefficient b. Specify the competing hypotheses in order to determine whether the population correlation coefficient is significantly different from zero c-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places) est statistic 0-2, At the 5% significance level, what is the conclusion to the test? Are the returns on the mutual funds significantly correlated? Reject Ho; there is enough evidence to state the returns are correlated. Reject Ho: there is not enough evidence to state the retuns are correlated Do not reject Ho: there is not enough evidence to state the returns are correlated. Do not reject Ho: there is enough evidence to state the retums are correlated.

Answer 1

Hello,  

Correction formula is as ,

r=Sxy/Sx.Sy

= 305.64/27.74 x 12.52

= 305.64/347.3048

=0.88

The correlation between x and y is 0.88

B)

Number 3 hypothesis is correct, we can test the population correction coefficient is zero or non zero

C-1 )

$t=\frac{r. \sqrt{n-2}}{ \sqrt{1-r^{2}}}$

=3.21

P-value for the above test statistics with n-2 df is 0.04899

The correlation coefficient is significant.

C-2)

First option is correct .

Thanks.