A sales manager wanted to determine if increasing sales commissions by 5% would increase employee satisfaction. Her analyst determined the p-value was 0.04. (Use α = 0.05.)

Based on the above output, what is the correct conclusion for the Wilcoxon Signed Rank Test?

a. We do not have evidence that there is a difference in population median employee satisfaction rating before and after the commission change.
b. We do not have evidence that there is a difference in sample median employee satisfaction rating before and after the commission change.
c. We have evidence that there is a difference in population median employee satisfaction rating before and after the commission change.
d. We have evidence that there is a difference in sample median employee satisfaction rating before and after the commission change.

Answer:

c. We have evidence that there is a difference in population median employee satisfaction rating before and after the commission change.

Step-by-step explanation:

Pvalue is less than the alpha-level:

If the pvalue is less than the alpha-level, we have that there is sufficient evidence of the hypothesis for the population mean/median/standard deviation we are testing.

In this question:

Pvalue less than the alpha-level, so there is evidence that there is a difference in the population median. This means that the correct answer is given by option C.

The correct conclusion is: c. We have evidence that there is a difference in population median employee satisfaction rating before and after the commission change.

The given parameters are:

[tex]\mathbf{p = 0.04}[/tex] --- the p-value

[tex]\mathbf{\alpha = 0.05}[/tex] --- the significance value or the alpha level

From the options, we understand that the test parameter is the population median

By comparison, the p-value (0.04) is less than the alpha level (0.05)

When the p-value is less than the alpha-level, then it means that there is enough evidence of the hypothesis for the population parameter that is being tested.

Since the p-value is less than the alpha level, then it means that there is enough evidence to show the difference in the population median.

Hence, option (c) is correct

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MY
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