Question

# A study was conducted to see if students’ writing skills continue to improve as the academic...

A study was conducted to see if students’ writing skills continue to improve as the academic year progresses. English 101 students were asked to write essays throughout the year in September, December, March and June. The scores were compared to see if there is any improvement in this one-year course. Was there a significant improvement?

The appropriate test for this problem is:

 one-way ANOVA

repeated measurements

 Student September December March June 1 17 23 21 24 2 25 21 21 24 3 24 16 21 29 4 18 18 25 27 5 25 21 24 24 6 25 25 16 25 7 24 15 23 22 8 24 21 19 23 9 20 17 16 28 10 24 22 21 22 11 16 24 25 29 12 18 24 23 24 13 15 16 22 27 14 23 24 22 22 15 21 24 20 25 16 22 16 25 26 17 16 16 20 23 18 24 22 22 27 19 19 23 23 27 20 19 17 25 25 21 20 17 19 22 22 22 19 25 24 23 15 24 22 26 24 22 21 15 26 25 25 16 24 22 26 15 22 25 23 27 15 17 25 29 28 18 18 19 23 29 17 17 21 29 30 19 17 15 26 31 19 16 18 26 32 22 21 16 29 33 16 19 19 29

The obtained statistic is:

 F = 24.17
 F = 12.71
 F = 21.47
 F = 17.42

The associated p value is:

 < .05
 < .01
 < .001
 < .0001

Decision is:

 reject the null
 retain the null

Conclusion is:

 1) March scores are significantly lower than the rest of the months
 2) December scores are significantly higher than September scores
 3) March scores are significantly higher than September scores
 4) June scores are significantly higher than the rest of the months
 5 )no conclusion can be drawn

Following is the output of one way ANOVA:

 Anova: Single Factor SUMMARY Groups Count Sum Average Variance September 33 664 20.12121212 12.10984848 December 33 649 19.66666667 10.04166667 March 33 697 21.12121212 9.984848485 June 33 837 25.36363636 5.863636364 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 670.3863636 3 223.4621212 23.52232855 3.43E-12 2.675387 Within Groups 1216 128 9.5 Total 1886.386364 131

The F test statistics is:

F = 23.52

The p-value is less than 0.0001

p-value < 0.0001

Reject null hypothesis.

5 )no conclusion can be drawn

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