Question

A data analyst is conducting a study to determine if the mean number of courses taken in a college semester is statistically the same between freshmen, sophomores, juniors, and seniors.

To collect data for this ANOVA test, the statistician randomly selects students attending college and records their year and the number of courses each is taking in the current semester, as shown in the table below. Assume the conditions necessary for a one-way ANOVA are met. Complete the ANOVA table below, rounding your answers to three decimal places.

Freshman	Sophomore	Junior	Senior
5	5	5	4
4	6	6	5
6	6	5	3
7	5	4	4
4	5	5	4
6	4		5
5			5
5

Answer 1

From the given information, Freshman Sophomore Senior Junior 5 6 Null hypothesis, H:44 = 4 = 4 = 44 (The mean number of courses taken in a college semester is statistically the same between freshmen, sophomores, juniors, and seniors) Alternative hypothesis, H: At least one mean is different from others.

Use MS Excel to perform the ANOVA one way analysis, One factor ANOVA Meann 5.3 5.2 6 5.0 5 4.3 7 4.9 26 Std. Dev 1.04 Freshman 0.75 Sophomore 0.71 Junior 0.76 Senior 0.89 Total ANOVA table Source Between Within Total SS 4.084 15.762 19.846 df 3 22 25 MS 1.361 0.716 F 1.900 p-value 0.159 From the above table, the F-test statistic value is: 1.900. The degrees of freedom is, v, = 3 and v2 = 22

Calculate the F-critical value (Use MS Excel function) F-critical = (=FINV(0.05,3,22)) = 3.049 Decision: Fail to reject H, because, the F-test statistic (1.900) is less than the critical value (3.049). Conclusion: There is not enough evidence to conclude that the mean number of courses taken in a college semester is statistically the different.