3. In a study of school attitude, fifth-grade students representing five ethnic

Question

3. In a study of school attitude, fifth-grade students representing five ethnic groups from twenty-six school districts in Colorado were compared. The following table is the summary statistics for the studv ni 138 Y 54.955.8 s2 38.4 33.6 American Black Hispanic Indians Orientals White 52 54.5 39.7 21 55.1 27.0 534 2.367 55.6 27.0 Test to see if the different ethnic groups had the same mean on the scores of the school attitude, using = .01. For this test, specify the null and alternate hypotheses that are being tested, construct an ANOVA table, specify the appropriate critical value for the test, and clearly state the conclusion of the test in the context of the problem.

Explanation / Answer

here for 0.01 and (n-1=5-1=4) degree of freedom in numerator and (138+534+52+21+2367-5=3107) degree of freedom critical value F =3.3252

applying one way ANOVA on above data:

as test statistic F =1.353 not in critical region we can not reject that all means are equal.

we do not have sufficient evidence to conclude that at least one group has different mean on the scores of the school attitude.

i ni Xi Si^2 ni*(Xi- grand mean)^2 (ni-1)*Si^2 black 138 54.9 38.400 64.097 5260.800 Hispanic 534 55.8 33.600 25.489 17908.800 American Indian 52 54.5 39.700 60.824 2024.700 Orientals 21 55.1 27.000 4.869 540.000 White 2367 55.6 27.000 0.808 63882.000 grand mean 55.582 156.088 89616.300 SSG SSE Source of variation SS df MS F treatment 156.088 4 39.022 1.353 error 89616.300 3107 28.843 total 89772.388 3111

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