In the digktal age of marketing, special care must be taken to make sure that programmatic ads appearing ethical values among individuals specializing in marketing $($higher scores indicate higher ethical values$).$

$($a$)$ Use $=0\mathrm{.}05$ to test for significant differences in perception among the three groups.

Find the value of the test statistic.

$6\mathrm{.}51$

State your conclusion.

State your conclusion. Reject $H_0.$ There is not

Do not reject $H_0.$ There is not sufficient evidence to conclude that the mean perception score is not the same for the throe groups of speoialists.

O Do not reject $H_D.$ There is sufficient evidence to conclude that the mean perception score is not the same for the three groups of specialists.

$($b$)$ Use Fisher's LSD and the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experimentwise error rate of $0\mathrm{.}05$ is desired.

Find the comparisomwise error rate. $($Round your answer to $4$ decimal places.$)$

Find the p$-$value for the hypothesis test for the difference between means for each pair of machines.