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 $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-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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Critical values Do not rej...

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