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

question 71

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 are given scores on both the mathematics section and the verbal section of a standardized test. The data for a random sample of students is given below. $\begin{array} { l l l l l l l l l l } \text { Mathematics } & 347 & 440 & 327 & 456 & 427 & 349 & 377 & 398 & 425 \\ \hline \text { Verbal } & 285 & 378 & 243 & 371 & 340 & 271 & 294 & 322 & 385 \end{array}$ At the 5% significance level, do the data provide sufficient evidence to conclude that there is a difference between the mean math score and the mean verbal score?

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Definitions:

Profit-Maximizing Output

The level of production that maximizes a firm’s profits, determined by the intersection of marginal cost and marginal revenue.

Total Revenue

The total income earned by a firm from selling its products or services, calculated as the quantity sold multiplied by the selling price.

Marginal Revenue

The additional income earned by selling one more unit of a product or service.

Minimum AVC

The lowest point on the Average Variable Cost curve, indicating the most efficient scale of production where variable costs per unit are minimized.