Preliminary Data Analyses Indicates That Use of a Paired Wilcoxon $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$

question 64

Essay

Preliminary data analyses indicates that use of a paired Wilcoxon signed-rank test is reasonable. Perform the hypothesistest by using a paired Wilcoxon signed-rank test. Assume that the null hypothesis is $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-Students take a math test before and after tutoring. The data for a random sample of students is given below. $$\begin{array} { c | l l l l l l l l l } \text { Before } & 54 & 72 & 59 & 82 & 46 & 80 & 63 & 36 & 44 \\ \hline \text { After } & 68 & 70 & 67 & 78 & 55 & 90 & 63 & 52 & 40 \end{array}$$ At the 2.5% level of significance, do the data provide sufficient evidence to conclude that the mean score before the tutoring is lower than the mean score after the tutoring?

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Definitions:

Disposed

This term refers to the action of getting rid of an asset or property, often through a sale, exchange, retirement, or destruction.

Goodwill

An intangible asset that arises when a business is acquired for more than the fair value of its net identifiable assets, reflecting the company's reputation, customer relations, and other non-physical assets.

Assets And Liabilities

Elements of a company's financial statements where assets represent resources owned, and liabilities represent obligations owed to others.

Depletion

The allocation of the cost of natural resources over the period of their extraction or harvesting, recognizing the exhausting nature of these assets.