## Related questions with answers

Consider the following competing hypotheses and accompanying sample data.

$\begin{aligned} &H_0: \rho_S \leq 0 \\ &H_A: \rho_S>0 \end{aligned} \quad r_S=0.64 \text { and } n=50$

a. What is the value of the test statistic and its associated $p$-value? Assume the normal approximation for $r_s$.

b. At the $1 \%$ significance level, what is the conclusion?

Solution

VerifiedThis two-part exercise gives us the competing hypotheses and the value of the sample Spearman rank correlation, relating to a Spearman rank correlation test being conducted. The sample size is $n=50.$

In this part of the exercise, we are tasked to calculate the test statistic for the test, assuming the normal approximation for $r_{S}$. We also need to compute its associated p-value.

*Why can we assume normal approximation for $r_{S}$?*
*What role does the p-value play in a hypothesis test?*

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