A researcher wants to investigate whether the amount of alcohol consumed by first-year college students has an impact on their grades. To study this, the researcher first categorized alcohol consumption as one of the following four categories: abstain (no alcohol consumption), light consumption (less than 2 drinks/ week), medium consumption (3-6 drinks/week), and heavy consumption (more than 6 drinks/week). A survey was then given out to 34 random freshmen asking them their current grade point average (GPA) as well as an estimate of the amount of alcohol they consumed each week. The results are provided in Table 10.9.

Is there a difference in the amount of alcohol consumed and the GPA for firstyear college students? In order to answer this question,

a. State the appropriate null and alternative hypotheses.

b. How would you describe the factor? And how many factor levels are there?

c. Find the SSE and the MSE.

d. Find the SSTR and the MSTR.

e. Find the number of degrees of freedom for the numerator and the number of degrees of freedom for the denominator.

f. Find the \(p\)-value and interpret it within the context of the problem.

g. Check any relevant model assumptions.

h. How big of a sample would be needed to find a minimum difference of 0.50 GPA points?

Table 10.9

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First-Year GPA By Amount of Alcohol Consumption Abstain 2.35 Light 3.45 Medium Heavy 2.48 2.04 3.41 2.68 2.65 2.65 3.26 2.48 2.47 2.31 2.58 3.54 1.54 1.65 3.98 2.98 1.69 0.89 3.45 2.38 2.45 3.12. 3.26 3.25 3.01 3.00 3.58 2.89 2.45 2.36 3.39 2.65