Students completed a high school senior level standardizedalgebra exam. Major for students was also recorded. Data in termsof percent correct is recorded below for 32 students. We areinterested to see if there is any difference between students'high-school algebra test scores and subsequent declared collegemajor.

These students have now also justcompleted the same college-level calculus class and received agrade. We are therefore now alsointerested to see if there is any relationshipbetween the students' algebra test scores and their calculus coursegrades: On average, did students who tended to score higher on thehigh-school algebra test also finish the course with higher grades?Conveniently, only one student of each major received the samegrade (see table - for example, there is only one Education majorwho received a grad of A).

Use the Microsoft Excel \"Anova Single-Factor\" Data Analysis toolto conduct a 2-way ANOVA test for the data in thefollowing table:

Declared College Major
Grade	Education	Business/Management	Behavioral/Social Science	Fine Arts
A	62	89	68	87
A-	81	88	71	57
B+	75	82	52	62
B	58	69	50	64
B-	67	59	22	28
C+	48	73	31	29
C	16	40	42	30
C-	26	45	16	15

1. What are your two null hypotheses in this study?
2. What are your two corresponding alternate hypotheses? Use thephrase \"at least one\" in each of your hypothesis statements.
3. What level of significance did you choose and why?
4. What are your F_crit values?