shown in the accompanying table; the higher the adindex value, the more likeable the ad$.$ State your findings and conclusions. Assume $=0\mathrm{.}05.$

Compute the descriptive statistics. Find the mean of the adindex ratings for cola A$.$

$($Round to two decimal places as needed.$)$

Find the mean of the adindex ratings for cola B$.$

Mean after workshops $=($Round to two decimal places as needed.$)$

Find the mean of the difference of the adindex ratings for cola A and cola B$.($Assume the difference to be the cola A data value minus the cola B data value$)$

Mean of the difference $=($Round to two decimal places as needed.$)$

Find the variance of the cola A adindex ratings.

$($Round to two decimal places as needed.$)$

Find the variance of the cola $B$ adindex ratings.

$($Round to two decimal places as needed.$)$

Find the variance of the difference of the adindex ratings for cola A and cola B$.$

$($Round to two decimal places as needed.$)$

Perform a paired t test. Let ${}_1$ be the population mean adindex rating for cola A and let ${}_2$ be the population mean adindex rating for cola $B.$ What are the null and alternative hypotheses?

$O$ A

$\{\begin{array}{c}\text{:}[H_0\text{:}{}_D=0]\\ H_1\text{:}{}_{D}0\end{array}($ where ${}_D={}_1-{}_2)$

C$.H_0$:${}_D,0$

$H_1$:${}_D,=0($where $\{$:${}_D={}_1-{}_2)$

$H_1$:${}_D=0$

Determine the test statistic, tSTAT.

Find the p$-$value for the test statistic.

The p$-$value is $.$

$($Round to three decimal places as needed.$)$

State your conclusion.

$H_0.$ There

$H_0.$ There

Do not reject

Reject

B$.$ where $\{$:${}_D={}_1-{}_2)H_1$:${}_D>0$

D$.H_0$:${}_{D}0($where $\{$:${}_D={}_1-{}_2)H_1={}_D<mn\; id="EditorElement\_595881">0</mn>$

Data table of the adindex ratings

$\backslash$table$[[$Cola A$,$Cola B$,$Cola A$,$Cola B$],[62,69,86,84],[89,83,88,88],[60,75,88,66],[87,71,78,94],[89,71,62,85],[83,78,67,82],[81,92,72,79],[81,69,73,91],[65,74,86,83],[79,64,61,78],[81,73,66,86],[60,83,73,82],[80,73,60,70],[61,86,72,84],[70,71,70,78],[77,68,63,67],[82,79,77,],[61,67,,]]$

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Done