1. Information regarding the ACT scores ofsamples of students in three different
ID: 2915575 • Letter: 1
Question
1. Information regarding the ACT scores ofsamples of students in three different
majors is given below.
Major
Management
Finance
Accounting
Sample size
12
9
12
Average
24
25
26
Sample variance
18
7
10
a. Compute the overall sample mean .
b. State the null and alternative hypothesis to be tested.
c. Set up the ANOVA table for this problem including the teststatistic.
d. The null hypothesis is to be tested at 95% confidence. Usethe critical value
approach to test it. What do you conclude?
e. Determine the p-value and use it for the test.
Management
Finance
Accounting
Sample size
12
9
12
Average
24
25
26
Sample variance
18
7
10
Explanation / Answer
a)The sample mean is 15.89 b)Null hypothesis:There is no difference between Act scoresand three majors H1:There is difference between Act scoresand three majors c) ANOVA Source of Variation SS df MS F P-value F crit Between Groups 28.22222 2 14.11111111 0.202229299 0.822255 5.14325285 Within Groups 418.6667 6 69.77777778 Total 446.8889 8 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 28.22222 2 14.11111111 0.202229299 0.822255 5.14325285 Within Groups 418.6667 6 69.77777778 Total 446.8889 8d)The critical value is 5.14 .The 95% confidenceinterval ctitrical value is 1.645 The p-value 0.82255 there fore reject the nullhypothesis ANOVA Source of Variation SS df MS F P-value F crit Between Groups 28.22222 2 14.11111111 0.202229299 0.822255 5.14325285 Within Groups 418.6667 6 69.77777778 Total 446.8889 8
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