5. (10 Points) The table below shows scores on the first quiz (maximum score 10

Question

5. (10 Points) The table below shows scores on the first quiz (maximum score 10 points) in a beginning French course. Students in the course are grouped as follows. Group A: Never studied foreign language before, but have good English skills. Group B: Never studied foreign language before, but have poor English skills. Group C: Studied other foreign language before. Group A 4 6 8 B12 3 C 9 10 8 The SPSS output given below provides results of an ANOVA. Based on this output answer the following questions. (a)What are the values for the sum of squares between and the sum of squares within and their degrees of freedoms? b) State the null and altermative hypotheses being tested by the F-statistic in the ANOVA table (c) Is there a significant difference between groups using 05. (d) If the differences are significant, use the Tukey's method to see which groups are different. Compare the results with that of the Bonferroni method.

Explanation / Answer

(a)
From the Anova output, Sum of squares between is 74.00
Sum of squares within is 12.00

Degree of freedom of between groups = 2
Degree of freedom of within groups = 6

(b)

Null hypotheses H0 : The average scores on the first quiz is statistically equal across the three groups of students.

Alternative hypotheses H1 : Atleast one average scores on the first quiz is statistically different across the three groups of students.

(c)

The P-value of F statistic is 0.003 which is less than the significance level of 0.05, so we reject the null hypothesis and conclude that atleast one average scores on the first quiz is statistically different across the three groups of students.

(d)

By Tukeys HSD output, the confidence interval of (group 2, group 3) and (group 1, group 2) does not contain 0. So, (group 2, group 3) and (group 1, group 2) are significantly different by Tukeys HSD method. That is, group 2 is significantly different from group 1 and group 3.

By Bonferroni output, the confidence interval of (group 2, group 3) and (group 1, group 2) does not contain 0. So, (group 2, group 3) and (group 1, group 2) are significantly different by Bonferroni method. That is, group 2 is significantly different from group 1 and group 3.

The results of Bonferroni and Tukey's HSD method are same.

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