The following data represent the results from an independent-measures study comparing three treatment conditions. Treatment I II III 5 2 7 N = 24 1 6 3 G = 72 2 2 2 ∑X² = 292 3 3 4 0 5 5 1 3 2 2 0 4 2 3 5 M = 2 M = 3 M = 4 T = 16 T = 24 T = 32 SS = 16 SS = 24 SS = 20
The following data represent the results from an independent-measures study comparing three treatment conditions. Treatment I II III 5 2 7 N = 24 1 6 3 G = 72 2 2 2 ∑X² = 292 3 3 4 0 5 5 1 3 2 2 0 4 2 3 5 M = 2 M = 3 M = 4 T = 16 T = 24 T = 32 SS = 16 SS = 24 SS = 20
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 4GP
Related questions
Question
9. Gravetter/Wallnau/Forzano, Essentials - Chapter 12 - End-of-chapter question 12
The following data represent the results from an independent-measures study comparing three treatment conditions.
|
Treatment
|
|
||
|---|---|---|---|
|
I
|
II
|
III
|
|
| 5 | 2 | 7 | N = 24 |
| 1 | 6 | 3 | G = 72 |
| 2 | 2 | 2 | ∑X² = 292 |
| 3 | 3 | 4 | |
| 0 | 5 | 5 | |
| 1 | 3 | 2 | |
| 2 | 0 | 4 | |
| 2 | 3 | 5 | |
| M = 2 | M = 3 | M = 4 | |
| T = 16 | T = 24 | T = 32 | |
| SS = 16 | SS = 24 | SS = 20 |
Use an ANOVA with α = .05 to determine whether there is a significant mean difference between the two treatments. (Round to two decimal places where needed.)
|
Source
|
SS
|
df
|
MS
|
F
|
Fcriticalcritical
|
|---|---|---|---|---|---|
| Between treatments |
|
|
|
|
|
| Within treatments |
|
|
|
||
| Total |
|
|
F Distribution
Numerator Degrees of Freedom = 6
Denominator Degrees of Freedom = 16
0.01.02.03.04.05.06.07.08.09.010.011.012.0F
Conclusion:
Reject the null hypothesis; there are no significant differences among the three treatments.
Fail to reject the null hypothesis; there are significant differences among the three treatments.
Reject the null hypothesis; there are significant differences among the three treatments.
Fail to reject the null hypothesis; there are no significant differences among the three treatments.
Expert Solution
Step 1
| anova table | ||||||
| SS | df | MS | F | p-value | F-critical | |
| Between: | 16.00 | 2 | 8.00 | 2.80 | 0.0836 | 3.47 |
| Within: | 60.00 | 21 | 2.86 | |||
| Total: | 76.00 | 23 | ||||
| α = | 0.05 |
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