A random sample of males who finished the marathon is partitioned into three cat

Question

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   3432063.284   2   1716031.642   0.1668   0.8466   3.0804
Within groups 1110875649   108   10285885.639          
Total 1114307712   110              

1. What is the null hypothesis?

A.The three age groups have the same mean time.

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 mean time of the third group is larger the mean time of the remaining groups.

2. What is the alternative hypothesis?

A.The three age groups have times with means that are not all the same.

B.The three age groups have times with means that are all the same.

C.The three age groups have times with means that are all differ from each other.

3. Identify the P-value.

The P-value is_____

(Round to four decimal places as needed.)

4. 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 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 appear to be different.

C.The large P-value suggests that we should not reject the null hypothesis. The three population means do not appear to be different.

Explanation / Answer

Answer to each question in detailed form as below. Please let me know in case you have any doubts

1. The null hypothesis always tests equality between all variables. So, A. the 3 groups have the same mean time - is CORRECT

2. The alternate hypothesis tests exactly the opposite of null hypothesis : that all 3 variables are not equal.

Therefore, CORRECT answer is A

3. P-value is .8466. Please check the p-value in the table given in the question. I will let you know how to interpret it.

4. The p-value, if above .05 means that the result is not significant. This is interpreted as a failure to reject null hypothesis and conclude that the 3 population means do not appear to be different.

C is CORRECT

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