11.2 PROBLEMS 11.5 Compute a one-way ANOVA on the folowing dasa Determine the ob
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11.2 PROBLEMS 11.5 Compute a one-way ANOVA on the folowing dasa Determine the observed F value. Compare the observed Fvalue with the critical value and decide whether to reject the null hypothesis. Use a -5 11.6 Compute a one-vay ANOVA on the follawing data 14 10 6 14 9 12 1712 10 12 13 3 9 12613 17 1 Determine the observed F value. Compure the observed F value with the critical table F value and decide whether to reject the null hypothesis. Use a- 11.7 Develop a one- way ANOVA on the foillowing data. Determine the observed Fvalue. Compare it to the critical Fvalue and decide whether to reject the mull hypothesis. Usa i% level of significance. 11.8 Compute a one-wiry ANONA on the following data 27 31 Determine the observed Fvalue. Compare it to the critical table F value and decide whether to reject the null hypothesis. Perform a 1 ses for independent measures on the data. Compare the f ard F values Are the results different, a-05 11.9 Suppose you are using a completely randomiand design to study some There are five treatment levels and a total of 55 people in the study. Each treatment Source of Variance 83,39 Errot There are three treatment levels and a total of 17 people in the study Complete the following ANOVA table Use a-05 to find the table Fvalue and use the data to test the nul hypothesis 11.10 Suppase you are using a completely randoenized design to study some phemomenonExplanation / Answer
11.5
One-way ANOVA: Response versus Factor
Source DF SS MS F P
Factor 2 31.85 15.92 10.12 0.002
Error 14 22.03 1.57
Total 16 53.88
Observed F=10.12, Critical value=F0.05,2,14=3.7389
We reject null hypothesis since Observed F> critical value.
11.6
One-way ANOVA: Response versus Factor
Source DF SS MS F P
Factor 4 42.57 10.64 1.74 0.184
Error 18 109.87 6.10
Total 22 152.43
Observed F=1.74, Critical value=F0.01,4,18=4.5790
We accept null hypothesis since Observed F< critical value.
11.7
One-way ANOVA: Response versus Factor
Source DF SS MS F P
Factor 3 408.0 136.0 6.28 0.008
Error 12 260.0 21.7
Total 15 668.0
Observed F=6.28, Critical value=F0.01,3,12=5.9525
We reject null hypothesis since Observed F> critical value.
11.8
One-way ANOVA: Response versus Factor
Source DF SS MS F P
Factor 1 64.29 64.29 17.76 0.001
Error 12 43.43 3.62
Total 13 107.71
Observed F=17.76, Critical value=F0.01,1,12=4.7472
We reject null hypothesis since Observed F> critical value.
Two-Sample T-Test and CI: Response, Factor
Two-sample T for Response
Factor N Mean StDev SE Mean
1 7 29.00 1.73 0.65
2 7 24.71 2.06 0.78
Difference = mu (1) - mu (2)
Estimate for difference: 4.29
95% CI for difference: (2.07, 6.50)
T-Test of difference = 0 (vs not =): T-Value = 4.21 P-Value = 0.001 DF = 12
Both use Pooled StDev = 1.9024
Here also we reject null hypothesis since p-value=0.001<0.05
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