Question

Complete this exercise using the Seven Steps to Hypothesis Testing.

A university president collects data showing the number of absences over the past academic year for a random sample of 6 professors in the College of Engineering. He does the same for a random sample of 9 professors in the College of Business and for a random sample of 8 professors in the College of Fine Arts. Assuming an alpha of .05, is there a significant difference in absences among colleges?

Answer 1

There are no data values but i am giving you example, follow the steps with your values

	Engineering	Business	Fine Arts
	8	5	9
	10	7	10
	6	6	10
	8	7	9
	4	7	7
	8	6	5
		8	13
		8	7
		1
Mean	7.333	6.111	8.75
SD	2.066	2.147	2.435
n	6	9	8	23
SUM(X^2)	344	373	654	1371
SUM(X)	44	55	70	169
SS = (SUM(X^2)-SUM(X)^2/n)	21.3333333	36.8888889	41.5	99.72222222
	df	SS	MS	F
Between	2 (k-1)	29.495 (SSB = SST-SSW)	14.7475(MSB = SSB/df1)	2.957722468 (F = MSB/MSW)
Within	20 (n-k)	99.722 (SSW=Total SS)	4.9861 (MSW = SSW/df2)
Total	22 (n-1)	129.217 (SST=Total(SUM(X^2))-Total(SUM(X))^2/Total(n))

Hypothesis:

1)Ho: μ₁ = μ₂ = μ₃

2)Ha: Not all means are equal

3)Rejection region:

df1 = 2 and df2 = 20

F critical = 3.493 (Use F table)

If F stat > F critical, reject H0

4)Test:

F = 2.9577

5)Decision:

F = 2.958 ≤ Fc​ = 3.493, Do not reject H0

6)P value = 0.0749 (Use F table)

P value > 0.05, Do not reject H0

7)Conclusion:

There is not enough evidence to conclude that there a significant difference in absences among colleges at 5% significance level