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

question 18

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 $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-A test of abstract reasoning is given to a random sample of students before and after completing a formal logic course. The results are shown below. $\begin{array} { l l l l l l l l l l l } \text { Before } & 74 & 83 & 75 & 88 & 84 & 63 & 93 & 84 & 91 & 77 \\ \hline \text { After } & 73 & 77 & 70 & 77 & 74 & 67 & 95 & 83 & 84 & 75 \end{array}$ At the 5% significance level, do the data provide sufficient evidence to conclude that that the mean score after the course differs from the mean score before the course? Use the critical-value approach.

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Definitions:

Indifference Curve Analysis

A graphical representation of consumer preferences showing combinations of goods or services among which they are indifferent, demonstrating varying levels of utility.

Indifference Curves

Graphical representations of different bundles of goods between which a consumer is indifferent, portraying preferences.

Indifference Curve

A graphical representation showing different bundles of goods between which a consumer is indifferent, reflecting their preferences and utility.

Total Utility

The overall satisfaction or benefit a consumer receives from consuming a particular quantity of a good or service.