Question

A researcher is interested to learn if there is a relationship between the level of interaction a women in her 20s has with her mother and her life satisfaction ranking. Below is a list of women who fit into each of four level of interaction. Conduct a One-Way ANOVA on the data to determine if a relationship exists. State whether or not a relationship exists and why or why not. Explain in as much detail as possible.

No Interaction	Low Interaction	Moderate Interaction	High Interaction
2	3	3	9
4	3	10	10
4	5	2	8
4	1	1	5
7	2	2	8
8	2	3	4
1	7	10	9
1	8	8	4
8	6	4	1
4	5	3	8

Answer 1

answer:

Hypotheses are:

H0: Mean interaction of the four groups are same.

Ha: Mean interaction of the four groups are not same.

Follwoing table shows the mean, sd, and total of all the four grades:

	G1	G2	G3	G4
	2	3	3	9
	4	3	10	10
	4	5	2	8
	4	1	1	5
	7	2	2	8
	8	2	3	4
	1	7	10	9
	1	8	8	4
	8	6	4	1
	4	5	3	8
Total	43	42	46	66
Mean	4.3	4.2	4.6	6.6
SD	2.626785	2.347576	3.405877	2.91357

Let G shows the grade. Follwoing table shows the calculation for ANOVA:

	G	G^2
	2	4
	4	16
	4	16
	4	16
	7	49
	8	64
	1	1
	1	1
	8	64
	4	16
	3	9
	3	9
	5	25
	1	1
	2	4
	2	4
	7	49
	8	64
	6	36
	5	25
	3	9
	10	100
	2	4
	1	1
	2	4
	3	9
	10	100
	8	64
	4	16
	3	9
	9	81
	10	100
	8	64
	5	25
	8	64
	4	16
	9	81
	4	16
	1	1
	8	64
Total	197	1301

Here we have

Now

Now

Now

Degree of freedom:

Since there are four groups so we have k = 4 therefore

And since total number of observations are 40 so N = 40 therefore

For F = 1.5703 and degree of freedom 3, 36 P-value of the test is 0.2134. Since P-value is greater than 0.05 so we fail to reject the null hypothesis. That is on the basis of sample evidence we cannot conclude that there is a relationship between the level of interaction a women in her 20s has with her mother and her life satisfaction ranking.

Follwoing is the completed ANOVA table:

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	38.275	3	12.7583333	1.57025641	0.21343404	2.86626556
Within Groups	292.5	36	8.125
Total	330.775	39

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