A statistics instructor was interested in whether doing group work, homework, or

Question

A statistics instructor was interested in whether doing group work, homework, or no work has an effect on students' test scores in her class. She randomly assigned 15 students to three groups (5 students in each group) and these are the test scores they received (out of 25 possible points on the test).

92+80+49=221

a.How many orthogonal comparisons can you have in this analysis? (1 point)

b.What are the Null hypotheses associated with the orthogonal comparisons? (2 points)

c.Assign the correct weightings for each orthogonal comparison. (2 points)

d.Demonstrate that your orthogonal comparisons are independent. (2 points)

e.Compute the SS for each orthogonal comparison (don’t forget to start with computing the L) (4 points)

f.Fill in the source table with information for each orthogonal comparison. (2 points)

g.What are your conclusions? (2 points)

Homework Group work No work 20 15 9 15 16 11 18 17 10 16 19 11 23 13 8 Total 92 80 49 Grand Total

92+80+49=221

1 Anova: Single Factor 2 3 SUMMARY 4 5 Column 1 6 Column 2 7 Column 3 Groups Count SumAverage Variance 11.8 3.5 92 18.4 16 9.8 49 10 ANOVA 11 Source of Variation 12 Between Groups 13 Within Groups 14 15 Total MS P-value F crit 196.9333 2 98.46667 17.37647 0.000286 3.885294 12 5.666667 264.9333 14

Explanation / Answer

a. There are 15 orthogonal compatisons in this analysis.

b. Hypothesis :

   Ho : doing group work, homework, or no work has an no effect on students' test scores in her class.

   H1 : doing group work, homework, or no work has an effect on students' test scores in her class.

d. Group work, homwork and no work all are indpndent

    So orthogonal comparisons are independent.

e. From givn output

   SS between : 196.933

    SS within : 68

From above output table we got p value = 0.000286 which is less that significance level 0.05.

So we reject the null hypothsis

So we can conclude that doing group work, homework, or no work has an effect on students' test scores in her class.

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