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

question 26

Essay

Preliminary data analyses indicates that use of a paired t-test is reasonable. Perform the hypothesis test by using eitherthe critical-value approach or the P-value approach as indicated. Assume that the null hypothesis is $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-Five students took a math test before and after tutoring. Their scores were as follows. $$\begin{array} { c | r r r r r } \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\ \hline \text { Before } & 66 & 73 & 71 & 66 & 75 \\ \hline \text { After } & 70 & 82 & 69 & 69 & 87 \end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the mean score before tutoring differs from the mean score after tutoring? Use the critical-value approach.

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Definitions:

Intergroup Strife

Conflict and competition that arise among groups due to differences in interests, beliefs, or resources.

Economic Terms

Language and vocabulary that pertain to the discipline of economics, dealing with the production, distribution, and consumption of goods and services.

Political Terms

Specific terminology used within the context of politics to describe processes, ideologies, structures, and roles.

Ingroup Favoritism

A psychological pattern where individuals prefer and favor members of their own group over those from different groups.