four sororities took a random sample of sisters regarding their grade means for

Question

four sororities took a random sample of sisters regarding their grade means for the past term. the results are shown in the table below. using a significance level of 1% to test the claim that the difference in mean grades among the sororities.

a) what are the hypotheses for this test?

b) determine the test statistic (round to two decimal places)

c) find the p-value and interpret the result (round to four decimal places)

d) conclusion

sorority 1 sorority 2 sorority 3 sorority 4 2.17 2.63 2.63 3.79 1.85 1.77 3.78 3.45 2.83 3.25 4 3.08 1.69 1.86 2.55 2.26 3.33 2.21 2.45 3.18

Explanation / Answer

a) null hypothesis: all sororities have equal mean score.

alternate hypothesis: at least two of the sororities have different mean score.

b)applying one way ANOVA on above given data:

from above test stat F=2.2303

c) p value= 0.1241 . AS p value is greater then 0.01 level we can not reject null hypothesis

d) we do not have suffiicent evidence to conclude that there is difference in mean grades among the sororities.

Groups Count Sum Average Variance sorority 1 5 11.87 2.374 0.47648 sorority 2 5 11.72 2.344 0.37108 sorority 3 5 15.41 3.082 0.55417 sorority 4 5 15.76 3.152 0.32437 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 2.88732 3 0.96244 2.230323 0.124144 5.292214 Within Groups 6.9044 16 0.431525 Total 9.79172 19

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