Question

As part of its freshman orientation process, a college gives a math placement exam to incoming...

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 =

Homework Answers

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

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