Descriptive Statistics

We are interested in examining whether students from different races or ethnicities perform differently on the science test. Below are the descriptive statistics and ANOVA table for this analysis.

Descriptive Statistics

Race or ethnicity	Mean	N	Std. Deviation
Hispanic	44.9296	71	9.67578
Asian	53.6412	34	9.17778
Black	43.4172	58	9.10841
White	53.8352	437	8.70227
Total	51.7633	600	9.70618

ANOVA

Science score

This is the main question for this study:

I. Are the 4 groups different (omnibus F test)? Obtain the hypotheses and make your decision (reject or fail to reject) about them based on the results from the ANOVA table. What is your conclusion in English?

In addition, we are also interested in answering the following questions:

IIA. Is the performance of the White group different from the average performance of the rest three groups?

IIB. Is the average score of the two high-performing groups different from the average score of the two low-performing groups?

IIC. Do White and Asian students have different mean science scores?

For these problems, find contrast coefficients for each test and obtain the appropriate hypotheses, critical values, test statistic, and conclusion (decision and conclusion in English). Use the Bonferroni method and Alpha = .05.

III. Obtain 95% CI for the contrasts IIA, IIB, and IIC using the adjusted alpha levels from the Bonferroni method.

1

�

Sum of

Squares�

df�

Mean Square�

F�

Sig.�

�

Between Groups

Within Groups

Total�

9351.683

47080.050

56431.733�

3

596

599�

3117.228

78.993�

39.462�

.000�

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