Barbara Wants to Know Whether Students Will Learn Most Effectively $\alpha$

Barbara wants to know whether students will learn most effectively with soft music as background sound, as opposed to loud music or no music at all. In the following table are three independent random samples (different background sounds) of paired values on the covariate (X; pretest score) and the dependent variable (Y; posttest score). Conduct an ANOVA on Y, an ANCOVA on Y using X as a covariate, and compare the results ( $\alpha$ = .05). Determine the unadjusted and adjusted means.
$\begin{array}{c}{\text { Soft music }} \quad \quad {\text { Loud music }} \quad \quad {\text { No music }} \\\begin{array}{|c|c|c|c|c|c|}\hline X \quad \quad& Y \quad \quad& X \quad \quad& Y \quad \quad& X \quad \quad& Y \quad \quad\\\hline 75 & 89 & 50 & 57 & 64 & 72 \\\hline 42 & 49 & 43 & 52 & 70 & 79 \\\hline 34 & 52 & 56 & 62 & 32 & 48 \\\hline 61 & 70 & 48 & 65 & 65 & 87 \\\hline 45 & 66 & 59 & 64 & 67 & 80 \\\hline 70 & 83 & 27 & 35 & 42 & 53 \\\hline 75 & 90 & 65 & 71 & 71 & 85 \\\hline 58 & 73 & 54 & 68 & 74 & 82 \\\hline\end{array}\end{array}$