Question

The following scores represent the number of errors made by each person on a verbal learning task. Each person was assigned to one of three study groups Test the hypothesis that the different study groups all produce the same average number of errors.

Group              Error Scores

Group 1: 16, 7, 19, 24, 31

Group 2: 24, 6, 15, 25, 32, 24, 29

Group 3: 16, 15, 18, 19, 6, 13, 18

1. Calculate ∑X²

^2. Calculate (∑x^2)/N also written as G^2/N

3. Fill in the ANOVA source table with the SS, DF and MS for both between groups variance and within groups variance.

4. Compute the F ratio.

5. The critical value for F = 3.63   at the .05 level of significance. What decision should be made about H₀ ?

6. Use a Z statement to describe the results

7. Use a concise statement including the three Means to interpret the results.

8. How many factors and how many levels were in the questions asked?

Answer 1

Answers:

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Ans 1)

∑x2 = ∑x21 + ∑x22 + ∑x23 = 2203 + 3903 + 1695=7801

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Ans 2)

(∑x)2/N = 6069

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Ans 3)

ANOVA table is below the output,

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Ans 4)

test statistic F for one way ANOVA test

F=MSB / MSW

F = 141.1429 / 80.5397

F=1.75

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Ans 5)

here the critical value of F is 3.63 and the calculated value of F is 1.75

Here the F calculated is less than F critical which means our null hypothesis is accepted.

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