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

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.