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

Homework, Chapter 7, Problem 43

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562

601

590

578

600

585

584

584

588

570

593

579

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602

593

572

587

570

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592

565

597

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604

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580

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572

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583

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610

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612

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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.