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

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

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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