## Related questions with answers

The following table shows a portion of the monthly returns data (in percent) for 2010-2016 for two of Vanguard's mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund.

$\begin{array}{|c|c|c|} \hline \text { Date } & \text { Energy } & \text { Healthcare } \\ \hline \text { Jan-10 } & -4.86 & -0.13 \\ \hline \text { Feb-10 } & 1.50 & 0.58 \\ \hline \vdots & \vdots & \vdots \\ \hline \text { Dec-16 } & -0.30 & -5.26 \\ \hline \end{array}$

b. Specify the competing hypotheses in order to determine whether the population correlation coefficient is different from zero.

Solution

VerifiedWe need to develop the hypotheses that can be used to test whether the population correlation coefficient between the monthly returns for the Energy Fund and the Healthcare Fund differs from zero. Researchers work to reject the null hypothesis and they develop the alternative hypothesis in which they believe that it explains a behavior. Denote the population correlation coefficient with $\rho_{xy}$.

*Will the hypotheses be for a one-tailed or a two-tailed test?*

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