Use the Spearman Rank Correlation Coefficient to Determine Whether the Correlation

question 74

Essay

Use the Spearman rank correlation coefficient to determine whether the correlation between the given variables is
significant. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses.
Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and
interpret the decision in the context of the original claim.
-A manager wishes to determine whether there is a relationship between the distance traveled per month by the
sales representatives and the amount of sales generated per month. Can you conclude that there is a correlation
between distance traveled and sales generated? Use $$\alpha$$ = 0.05. $$\begin{array} { l | r r r r r r r r r } \text { Distance (hundreds of miles) } & 11 & 12 & 19 & 16 & 17 & 24 & 12 & 10 & 20 \\\hline \text { Sales (thousands of dollars) } & 40 & 42 & 87 & 71 & 74 & 70 & 57 & 64 & 129\end{array}$$

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Definitions:

Without Replacement

A sampling method where each selected item is not returned to the population before the next item is selected, affecting the outcomes' probabilities.

Probability

A measure of the likelihood of a particular event or outcome occurring, often expressed as a number between 0 and 1.

Red Chips

In finance, companies based in Mainland China that are incorporated internationally and listed on the Hong Kong Stock Exchange. In gaming, chips colored red typically represent a specific value.

Chosen Field

Chosen field refers to a specific area or discipline that an individual has selected to pursue professionally or academically.