Question

Age 40 50 60 Fitness 1 79.5 697.4 705 326.7 309.6 537.6 Fitness 2 676.6 682.9...

Age 40 50 60
Fitness 1 79.5 697.4 705
326.7 309.6 537.6
Fitness 2 676.6 682.9 752.3
195.8 436 1174
Fitness 3 1187.6 810.7 912.6
876.6 809.9 797.4
Average 557.133333 624.416667 813.15

With this data, could you please help me answer the questions below (Carry out a two-way analysis of variance):

14. What is the value of the F test statistic for testing the hypothesis that age, one average, has no effect on running time?  
15. What are the numerator degrees of freedom for that F statistic reported in Question 14?  
16. What are the denominator degrees of freedom for that F statistic reported in Question 14?  
17. What is the value of the F test statistic for testing the hypothesis that fitness, on average, has no effect on running time?  
18. What is the value of the F test statistic for testing the hypothesis that the effective age, if any, on running time does not depend on the runner's fitness?  
19. Should the null hypothesis that age has no effect on running time be rejected (1) or not rejected (0)? (Use α = 0.01 (significance level =1 %)
20. Should the null hypothesis that the effective age is independent of the effect of fitness be rejected (1) or not rejected (0)? (Use α = 0.01 (significance level =1 %)
21. What was the average running time for all 60-yr olds?  
22. What was the average running time for all men in fitness category 3?  
23. What was the mean time of the two 60-yr, category 3 runners?

Math   Statistics-And-Probability   
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Answer #1

here applying 2 way ANOVA from excel :Data-data analysis: 2 way ANOVA(with replication)

Source of Variation SS df MS F P-value
fitness 626465.5600 2 313232.7800 6.8803 0.0154
age 211383.7033 2 105691.8517 2.3216 0.1538
Interaction 333553.9867 4 83388.4967 1.8317 0.2070
Within 409735.6300 9 45526.1811
Total 1581138.8800 17

14) value of the F test statistic for age =2.3216

15() numerator degrees of freedom =2

16) denominator degrees of freedom =9

17_) value of the F test statistic =6.8803

18 e value of the F test statistic =1.8317

19) No, since p value 0.1538 < 0.01

20) No since p value 0.2070 < 0.01

21) average running time =813.15

22) average running time for all men in fitness category 3 =899.1333

23) mean time of the two 60-yr, category 3 runners =855

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