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

question 16

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 $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-The table below shows the weights, in pounds, of seven subjects before and after following a particular diet for two months. $$\begin{array} { c | r r r r r r r } \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\ \hline \text { Before } & 196 & 187 & 177 & 161 & 197 & 168 & 154 \\ \hline \text { After } & 189 & 178 & 175 & 166 & 183 & 170 & 142 \end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the diet is effective in reducing weight? Use the critical-value approach.

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Definitions:

Standard Error

A measure that quantifies the variation or dispersion of a sample mean from the population mean.

Population Proportion

The fraction or percentage of a population that possesses a certain property or characteristic.

Control Chart

A statistical tool used in quality control processes to monitor, control, and ascertain the stability of a process.

Defective Candy Bars

Candy bars that do not meet the production quality standards due to flaws.