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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

Liberal Arts

Sciences

575

Homework, Chapter 7, Problem 43
.docx

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

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.

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