Question

In: Statistics and Probability

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 Excel to calculate the degrees of freedom, critical value, and test statistic for the data set, rounding the critical value and test statistic to two decimal places.

Science Engineering Humanities Business
89 83 86 78
89 85 82 78
90 86 86 82
88 82 85 81
83 82 82 79
82 87 88 87
85 83 85 85
83 85 87 83
83 83 86 82
87 87 86 79
87 86 81 76
81 87 85 78
87 90 84 79
83 85 85 74
85 86 86 88
88 81 86 83
85 88 79 82
85 87 82 81
89 88 82 78
89 91 79 78

Numerator degrees of freedom = ?

denominator degrees of freedom =?

critical value = ?

test statistic = ?

Solutions

Expert Solution

using minitab we have the following output

One-way ANOVA: Science, Engineering, Humanities, Business

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.01

Equal variances were assumed for the analysis.


Factor Information

Factor Levels Values
Factor 4 Science, Engineering, Humanities, Business


Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 3 361.5 120.513 14.15 0.000
Error 76 647.3 8.518
Total 79 1008.9


Model Summary

S R-sq R-sq(adj) R-sq(pred)
2.91852 35.84% 33.30% 28.90%


Means

Factor N Mean StDev 99% CI
Science 20 85.900 2.751 (84.176, 87.624)
Engineering 20 85.600 2.683 (83.876, 87.324)
Humanities 20 84.100 2.594 (82.376, 85.824)
Business 20 80.550 3.546 (78.826, 82.274)

Pooled StDev = 2.91852

Numerator degrees of freedom = 3

denominator degrees of freedom =76

critical value = 4.050

test statistic = 14.15

since the value of test statistic is less then critical value we reject the null hypothesis .


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