Some apartments have reputations as party places, while others are more serious.

Question

Some apartments have reputations as party places, while others are more serious. You are curious to see if there is any difference in the average GPA of people who live in Baker, Charlie, Delta, and Adam. The following chart lists 7 GPA’s of randomly selected people. Use a=0.05 to test for differences among the GPA means for the four aparments.

Adam Baker Charlie Delta 2.420 2.303 3.063 2.833 3.733 2.912 3.250 3.650 2.795 3.215 2.529 3.289 1.683 3.069 2.750 3.533 2.353 2.629 3.200 2.638 3.045 2.929 1.786 2.500 2.333 2.571 2.706 3.046

Explanation / Answer

Sol:

We solve this by one way ANOVA test

Null hypothesis:

H0: GPA means for the four aparments are equal

Alternative hypotehsis:

H1:Atleast one of the GPA means for the four aparments are not equal.

Level of significance=0.05

Calculation f test statistic:

F

Used Excel To get the output

From table above

F calculated=1.014

Decison rule:

if p<0.05 Reject nul hypotjhesis

if p>0.05 Fail to reject null hypothesis

Calculation of p value

P value from above =0.403

P value>0.05

Fail to Reject null hypothesis

Accept Null Hypothesis.

Conclusion:
there is no sufficient evidence at 0.05 leve lof significance to support the claim he GPA means for the four aparments are different.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Adam 7 18.362 2.623143 0.420263 Baker 7 19.628 2.804 0.100392 Charlie 7 19.284 2.754857 0.255063 Delta 7 21.489 3.069857 0.1945 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.73838 3 0.246127 1.014729 0.40347 3.008787 Within Groups 5.821303 24 0.242554 Total 6.559683 27

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