Question

In: Statistics and Probability

Statistics exercises Friedman’s K/One-way repeated measures ANOVA 1. Suppose you are interested in learning if practice...

Statistics exercises

Friedman’s K/One-way repeated measures ANOVA

1. Suppose you are interested in learning if practice on the ACT improves test scores. You sample a random group of 10 people and ask them to take the ACT 1 time per week for 3 consecutive weeks. Use the data below to determine if practice improves test scores.

Participant

Test 1

Test 2

Test 3

1

18

23

24

2

20

22

26

3

21

24

23

4

19

25

28

5

20

21

23

6

19

22

25

7

20

20

20

8

21

23

25

9

28

27

29

10

25

27

26

  1. State the hypotheses
  1. Select an alpha level and one- or two-tailed
  1. Select and compute the appropriate statistic

  1. Report in APA style the df and p-value.
  1. Accept or reject the null and draw an inference if one is warranted.

Solutions

Expert Solution

H0: the ACT not improves test scores.

H1: the ACT improves test scores.

It is one tailed test

From the given data

Anova Table Alpha = 0.05
Source df SS MSS Var. Ratio F F-critic P-Value
B/w groups 2 73.267 36.633 13.9114 3.5546 0.00022
Within Group 27 196.2 7.2667
i) B/w Subject 9 148.8
ii) Error 18 47.4 2.633
Total: 29 269.4667

Test Statistic F = 3.5546

since P-value for two tailed = 0.00022 and P-value for 1-tailed is 0.0001 < alpha 0.05 so we reject H0

Thus we conclude that  the ACT improves test scores.


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