A random sample of males who finished the marathon is partitioned

into three categories with ages of​ 21-29, 30-39, and 40 or over. The times​ (in seconds) are obtained for the selected males. The analysis of variance results obtained from software are below. The significance level is 0.05 in testing the null hypothesis.

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

Between groups 3132063.284 2  1566031.642 0.1290 0.8791 3.0804

Within groups 1310875649 108 12137737.491 1314007712

Total 1314007712 110

a. What is the null​ hypothesis?
A.
The mean time of the third group is larger the mean time of the remaining groups.
B.
The mean time of the first group is larger the mean time of the remaining groups.
C.
The mean time of the second group is larger the mean time of the remaining groups.
D.
The three age groups have the same mean time.

b. What is the alternative​ hypothesis?
A.
The three age groups have times with means that are all the same.
B.
The three age groups have times with means that are not all the same.
C.
The three age groups have times with means that are all differ from each other.

c. Identify the​ P-value.
The​ P-value is ___? ​(Round to four decimal places as​ needed.)

d. Is there sufficient evidence to support the claim that men in the different age categories have different mean​ times?
A.
The large​ P-value suggests that we should not reject the null hypothesis. The three population means appear to be different.
B.
The large​ P-value suggests that we should not reject the null hypothesis. The three population means do not appear to be different.