The following table shows the annual returns for two of Vanguard's mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund. a. Calculate and interpret the sample correlation...

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The following table shows the annual returns for two of Vanguard's mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund.

a. Calculate and interpret the sample correlation coefficient rxy.


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


c. At the 5% significance level, what is the conclusion to the test? Are the returns on the mutual funds significantly correlated?




Answered Same DayDec 25, 2021

Answer To: The following table shows the annual returns for two of Vanguard's mutual funds: the Vanguard...

David answered on Dec 25 2021
128 Votes
Let X denote number of correct in n = 10 independent questions, where each has
a probability p = 0.25
We denote this by:
X ∼ Binomial(n = 10, p = 0.25)
Probability of x number of correct is:
P (X = x) =
(
n
x
)
px(1 − p)(n−x)
where
(
n
x
)
is combinatorial expression:(
n
x
)
=...
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