Question

Begin by re-writing the problem.  Minitab is required; attach or include your output. Use Word; you may handwrite equations. You may want to refer to the Minitab handout for Chapter 11, which may be found on Canvas.

1. Quarterly GPAs are compared for seven randomly chosen students in each of the four business majors at Catalyst University. Do the data show a significant difference in mean GPAs?  The data is in the file named GPA1.

GPA for Randomly Selected Students in Four Business Majors
Accounting	Finance	Human Resources	Marketing
2.48	3.16	2.93	3.54
2.19	3.01	2.89	3.71
2.62	3.07	3.48	2.94
3.15	2.88	3.33	3.46
3.56	3.33	3.53	3.50
2.53	2.87	2.95	3.25
3.31	2.85	3.58	3.20

a) At the 0.05 level of significance, determine if there is a difference in the GPAs by Business Major. State your hypotheses and show all 7 steps clearly. (8 points)

2. Give and interpret the p-value. (3 points)

3. Should Tukey pairwise comparisons be conducted?  Why or why not? (3 points)

4. If appropriate, use Minitab to produce Tukey pairwise comparison.  Write a few sentences with your conclusions from those comparisons.  (5 points)

5. Use Levene’s test to determine if the assumption of homogeneity of variances is valid.  Give the hypotheses, test statistic, p-value, decision and conclusion.  Use the 0.05 level of significance.  (8 points)

6. Verify with Minitab by attaching or including relevant output. (6 points)

Answer 1

Answer:

Given that:

Quarterly GPAs are compared for seven randomly chosen students in each of the four business majors at catalyst University.

The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one means is not equal

Since the p-value (0.0328) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a significant difference in the mean GPAs.

The Minitab output is:

Factor Information :

Factor	Levels	Values
Factor	4	Accounting,Finance,Human Resources,marketing

Analysis of Variance:

Source	DF	Adj SS	F-Value	Adj MS	P-Value
Factor	3	1.166	0.3887	3.44	0.033
Error	24	2.713	0.1131
Total	27	3.879

Model Summary:

S	R-sq	R-sq(adj)	R-sq(pred)
0.336240	30.06%	21.31%	4.80%

Means:

Factor	N	Mean	StDev	95% CI
Accounting	7	2.834	0.505	(2.572 , 3.097)
Finance	7	3.0243	0.1776	(2.7620 , 3.2866)
Human Resources	7	3.241	0.308	(2.979 , 3.504)
Marketing	7	3.367	0.266	(3.105 , 3.629)

Pooled StDev = 0.336240

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence:

Factor	N	Mean	Grouping
Marketing	7	3.367	A
Human Resources	7	3.241	A B
Finance	7	3.0243	A B
Accounting	7	2.834	B

Means that do not share a letter are significantly different.

The Levene's test output is:

Test for Equal Variances : Accounting , Finance , Human ....es , Marketing method

Null hypothesis All variances are equal

Alternative hypothesis All least one variance is different

Significant level    = 0.05

Bartlett's method used . This method is accurate for normal data only.

95% Bonferroni Confidence Intervals for Standard Deviations :

Sample	N	StDev	CI
Accounting	7	0.505267	(0.291774 , 1.44555)
Finance	7	0.177563	(0.102536 , 0.50800)
Human Resources	7	0.307703	(0.177687 , 0.88032)
Marketing	7	0.265939	(0.153571 , 0.76084)

Individual Confidence level = 98.75%

Tests:

Method	Test Statistic	p - value
Barlett	6.22	0.101

Since the p-value (0.101) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we can conclude that all variances are equal.