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# Homework: Chapter 7, Problem 43

**Homework: Chapter 7, Problem 43**

A college is trying to determine if there is a significant difference in the mean GMAT score of students from different undergraduate backgrounds who apply to the MBA program.

The Excel file GMAT Scores contains data from a sample of students. What conclusion can be reached using ANOVA?

**GMAT Scores**

**Undergraduate Major**

**Business**

**Liberal Arts**

**Sciences**

575

562

601

590

578

600

585

584

584

588

570

593

579

565

602

593

572

587

570

573

592

565

597

598

604

605

580

590

610

572

590

583

594

610

589

612

588

586

The Excel Data Analysis Tool for ANOVA single factor with repetition will be used to conduct the analysis,

From the statement, the null and alternative hypotheses are :

**Ho** : There is no difference in the mean GMAT scores for students of different undergraduate backgrounds
**Ha** : There is a difference in the mean GMAT scores for students of different undergraduate backgrounds

**DATA SUMMARY**

**Groups**

**Count**

**Sum**

**Average**

**Variance**

Business

13

7593

584.0769

134.5769

Liberal Arts

7

4004

572

55.6667

Sciences

18

10719

595.5

90.8529

**ANOVA ANALYSIS**

**Source of Variation**

**SS**

**df**

**MS**

**F**

**P-value**

**F crit**

Between Groups

2983.9453

2

1491.9727

14.95

0.0000

3.27

Within Groups

3493.4231

35

99.8121

Total

6477.3684

37

**p-value = 0.00 **

Let α = 0.05 5% level of significance

0.0 < 0.05

that is, p-value < 0.05
Hence, ** Ho is rejected **

From the analysis above, at 5% (0.05) level of significance, it’s clear there is a difference in the mean GMAT scores for students of different undergraduate backgrounds. This means that the GMAT scores for students of different undergraduate backgrounds are different.