Question

Please help me with problem 3 (a-d). Thank you!

Answer 1

Using the spread sheet we can easily get the answers:

The statistical section helps find answers by putting the accurate formula or the graphing calculator.

ANOVA      

Source of Variation SS   df     MS         F        P-value      F crit

Between Groups 1471.33    2 735.68 11.59   0.001072834 3.7389

Within Groups 888.55 14 63.4677      

Total              2359.882 16    

The APA style refers to Times New Roman Font 12 pts.

The effect size of the result is 0.6233 medium

Part A

ANOVA      

Source of Variation SS   df     MS F        P-value F crit

Between Groups 1471.33    2 735.68 11.59   0.001072834 3.7389

Within Groups 888.55 14 63.4677      

Total        2359.882 16    

1) The null and alternative hypotheses are

H0: u1=u2=u3

Ha: Not all means are equal

2) The significance level is alpha = 0.05

3) The test statistic F = sb²/sw²

Which if H0 is true has an F distribution with ν1=2 and  v2= 14 degrees of freedom.

The computations are

Anova: Single Factor            

Groups Count Sum Average            Variance  

Column 1      6          373    62.16666667      78.96666667  

Column 2 4 324              81             60.66666667  

Column 3 7 402        57.42857143     51.95238095  

     

     

ANOVA      

Source of Variation SS   df     MS F        P-value F crit

Between Groups 1471.33    2 735.68 11.59   0.001072834 3.7389

Within Groups 888.55 14 63.46768707      

Total        2359.882353 16  

5) The critical region is F ≥ F(0.05)(2,14) = 3.74

6) Conclusion:

Since the computed value F= 3.73 does not fall in the critical region F> 3.74 so we accept H0 and conclude that there is no significant difference in the three means.

Part D: The effect size of the result is 0.6233 medium and  calculated by

η²= ss between/ ss between + ss error

η²= 1471/1471+889

η²= 0.6233

For further understanding of ANOVA click

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