Question

Recall lab experiment described in 13.2. The response variable is weight gains (in grams). There are 3 groups of lab animals, each with 5 test animals. Data are shown in Table. Complete a one way analysis of variance for this problem. Sow all hypothesistesting steps and return results. Data from exercis 13.4: Weight gain in lab mice over one month period

Group 1 (standard) 9.09, 9.96, 9.72, 9.64, 8.14

Group 2 (junk food) 10.21, 10.48, 13.01, 12.74, 12.58

Group 3 (organic) 9.03, 9.55, 12.35, 9.33, 9.51

Answer 1

Hypotheses are:

H0: Weight gain by mice is same for all three groups.

Ha: Weight gain by mice is different for at least one group.

Let us assume level of significance : 0.05

Following table shows the calculations:

	Group 1	Group 2	Group 3
	9.09	10.21	9.03
	9.96	10.48	9.55
	9.72	13.01	12.35
	9.64	12.74	9.33
	8.14	12.58	9.51
Total	46.55	59.02	49.77

and

	G	G^2
	9.09	82.6281
	9.96	99.2016
	9.72	94.4784
	9.64	92.9296
	8.14	66.2596
	10.21	104.2441
	10.48	109.8304
	13.01	169.2601
	12.74	162.3076
	12.58	158.2564
	9.03	81.5409
	9.55	91.2025
	12.35	152.5225
	9.33	87.0489
	9.51	90.4401
Total	155.34	1642.151

So we have

So,

Now

Now

Since there are 3 different groups so we have k=3. Therefore degree of freedoms are:

-------------

Now

F test statistics is

The p-value is: 0.0154

Since p-value is less than 0.05 so we reject the null hypothesis at 5% level of significance.