Question

(12pts) An experiment was conducted to examine the effect of age on heart rate when a person is subjected to a specific amount of exercise. Ten male subjects were randomly selected from four age groups: 10-19, 20-39, 40-59, and 60-69. Each subject walked on a treadmill at a fixed grade for a period of 12 minutes, and the increase in heart rate, the difference before and after exercise, was recorded (in beats per minute). Answer the questions based on the printout.

	N	Mean	Std. Deviation
10-19	10	30.9000	5.19508
20-39	10	27.5000	4.88194
40-59	10	29.5000	4.69633
60-69	10	28.2000	5.57375
Total	40	29.0250	5.07122

ANOVA
Increase in heart rate (in beats per minute)
	Sum of Squares	Df	Mean Square	F	Sig.
Between Groups	67.475	3	22.492	.866	.468
Within Groups	935.500	36	25.986
Total	1002.975	39

(2pts) Write the null and alternative hypotheses for this test.

(2pts) Give the test statistic and P-value for this problem.

(4pts) Write your conclusions for this test in terms of the story.

(4pts) The output for the Bonferroni Multiple Comparisons procedure is given below. If it is appropriate to use that at this point, explain why and give the conclusions to the procedure. If it is not appropriate to use Bonferroni at this point, explain why not.

Multiple Comparisons
Dependent Variable:   Increase in heart rate (in beats per minute)
Bonferroni
(I) AgeGroup	(J) AgeGroup	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
					Lower Bound	Upper Bound
10-19	20-39	3.40000	2.27974	.867	-2.9650	9.7650
	40-59	1.40000	2.27974	1.000	-4.9650	7.7650
	60-69	2.70000	2.27974	1.000	-3.6650	9.0650
20-39	10-19	-3.40000	2.27974	.867	-9.7650	2.9650
	40-59	-2.00000	2.27974	1.000	-8.3650	4.3650
	60-69	-.70000	2.27974	1.000	-7.0650	5.6650
40-59	10-19	-1.40000	2.27974	1.000	-7.7650	4.9650
	20-39	2.00000	2.27974	1.000	-4.3650	8.3650
	60-69	1.30000	2.27974	1.000	-5.0650	7.6650
60-69	10-19	-2.70000	2.27974	1.000	-9.0650	3.6650
	20-39	.70000	2.27974	1.000	-5.6650	7.0650
	40-59	-1.30000	2.27974	1.000	-7.6650	5.0650

Answer 1

(2pts) Write the null and alternative hypotheses for this test.

Ho:All the four age groups mean heart rate was same

Ha:atleast one of the four age groups mean heart rate was different

(2pts) Give the test statistic and P-value for this problem

F(3,36)=0.866

p=0.468

(4pts) Write your conclusions for this test in terms of the story.

p=0.468

p>0.05

Do not reject H0.

Accept Ho.

there is no suffcient statistical evidence at 5% level of signficance to conclude that there is effect of age on heart rate when a person is subjected to a specific amount of exercise.

4pts) The output for the Bonferroni Multiple Comparisons procedure is given below. If it is appropriate to use that at this point, explain why and give the conclusions to the procedure. If it is not appropriate to use Bonferroni at this point, explain why not.

If we conclude that ateast one of the 4 group means are different (by ONE way ANOVA) then only we can go for  Bonferroni Multiple Comparisons procedure .

But here in ANOVa we found that there is noeffect of age on heart rate when a person is subjected to a specific amount of exercise.

means all the 4 age group means are equal No need to conduct  Bonferroni Multiple Comparisons procedure .

which is also evident from the p values from Bonferroni Multiple Comparisons procedure that

all the 4 age group means are equal as all comapred means p values are greater than 0.05.