In: Statistics and Probability
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 =