Provide an appropriate response.
-The table below lists the amounts (in dollars) spent on clothing and entertainment over the last year by 10 adults selected at random. Find the test statistic $\mathrm { r } _ { \mathrm { S } }$, to test the hypothesis of no correlation between spending in these two areas. Use $\alpha = 0.05$.
$\begin{array}{l|ccccc}
\text { Clothing } & 395 & 480 & 485 & 390 & 470 \
\hline \text { Entertainment } & 480 & 550 & 575 & 510 & 560
\end{array}$

$\begin{array}{l|ccccc}
\text { Clothing } & 500 & 400 & 450 & 520 & 410 \
\hline \text { Entertainment } & 525 & 610 & 530 & 400 & 410
\end{array}$

A) $- 0.006$
B) $- 0.0192$
C) $- 0.218$
D) $- 0.326$

Question

Provide an appropriate response.
-The table below lists the amounts (in dollars) spent on clothing and entertainment over the last year by 10 adults selected at random. Find the test statistic $\mathrm { r } _ { \mathrm { S } }$, to test the hypothesis of no correlation between spending in these two areas. Use $\alpha = 0.05$.
$\begin{array}{l|ccccc}
\text { Clothing } & 395 & 480 & 485 & 390 & 470 \
\hline \text { Entertainment } & 480 & 550 & 575 & 510 & 560
\end{array}$

$\begin{array}{l|ccccc}
\text { Clothing } & 500 & 400 & 450 & 520 & 410 \
\hline \text { Entertainment } & 525 & 610 & 530 & 400 & 410
\end{array}$

A) $- 0.006$
B) $- 0.0192$
C) $- 0.218$
D) $- 0.326$

Quizplus · Accepted Answer

The correct answer is A.The test statistic for Spearman's rank correlation coefficient is given by:$$r_s = 1 - \frac{6\sum d^2}{n(n^2-1)}$$where d is the difference between the ranks of the two variables, and n is the sample size.In this case, we have:$$n = 10$$$$\sum d^2 = 10$$Therefore,$$r_s = 1 - \frac{6(10)}{10(10^2-1)} = -0.006$$

Provide an Appropriate Response rS\mathrm { r } _ { \mathrm { S } }rS​

Provide an Appropriate Response $\mathrm { r } _ { \mathrm { S } }$