Question

As part of its freshman orientation process, a college gives a math placement exam to incoming freshmen. The math department is interested in whether there is a statistically significant difference in the average exam score for students in different programs, at a level of α=0.01. The exam scores for random samples of science, engineering, humanities, and business majors are shown in the following table. The math department has confirmed that the samples were randomly selected and independent, that the populations are normally distributed, and that the population variances of scores are equal. Use a TI-83, TI-83 plus, or TI-84 calculator and the following table of critical values for the F-distribution to calculate the degrees of freedom, critical value, and test statistic for the data set, rounding the test statistic to two decimal places.

Critical Values of the F-Distribution for α=0.01

	Degrees of Freedom for the Numerator
Degrees of Freedom for the Denominator	1	2	3	4	5
30	7.56	5.39	4.51	4.02	3.70
31	7.53	5.36	4.48	3.99	3.67
32	7.50	5.34	4.46	3.97	3.65
33	7.47	5.31	4.44	3.95	3.63
34	7.44	5.29	4.42	3.93	3.61
35	7.42	5.27	4.40	3.91	3.59
36	7.40	5.25	4.38	3.89	3.57
37	7.37	5.23	4.36	3.87	3.56
38	7.35	5.21	4.34	3.86	3.54
39	7.33	5.19	4.33	3.84	3.53
40	7.31	5.18	4.31	3.83	3.51

Science	Engineering	Humanities	Business
87	88	85	82
79	89	84	78
84	88	91	80
83	86	84	78
89	89	83	78
87	87	79	79
91	94	91	74
83	90	81	79
85	86	82	83
86	86	91	79

Provide your answer below:

Numerator degrees of freedom = , denominator degrees of freedom = , critical value = , test statistic =

Answer 1

using excel>data>data analysis>one way anova

we have

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Science	10	854	85.4	11.6
Engineering	10	883	88.3	6.011111
Humanities	10	851	85.1	19.43333
Business	10	790	79	6
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	458.5	3	152.8333	14.20237	2.89E-06	4.377
Within Groups	387.4	36	10.76111
Total	845.9	39

Numerator degrees of freedom =3

, denominator degrees of freedom = 36

, critical value =4.38

, test statistic =14.20