Question

Statistics exercise

One-way BG ANOVA

    Suppose you would like to know if political party affiliation (democrat, republican, libertarian) has an effect on how people feel about the war in Afghanistan. You ask people to rate on a scale from 1-100 how much they support the war effort. Use the data below to see if the groups differed.

Democrats	Republicans	Libertarians
35	65	15
15	60	25
50	75	35
40	60	40
30	90	35
45	75	25
25	65	45
40	70	35

1. State the hypotheses

2. Select an alpha level and one- or two-tailed

3. Select and compute the appropriate statistic.

4. Report your findings in APA style

5. Accept or reject the null and draw an inference if one is warranted.

Answer 1

Answer:

Let us denote population means of the three groups by

We test the hypothesis that mean scale of all groups is same.

Null hypothesis:

against alternative hypothesis that group means are different from each other.

Let us test this hypothesis at 5% level of significance and the test is one tailed.

Group 1: (Democrat)

	Democrat	deviation	squared deviation
	35	0	0
	15	-20	400
	50	15	225
	40	5	25
	30	-5	25
	45	10	100
	25	-10	100
	40	5	25
Mean	35	ss	900

Variance of group 1:

Group 2: (Repluclicans)

	Replublicans	deviation	squared deviation
	65	30	900
	60	25	625
	75	40	1600
	60	25	625
	90	55	3025
	75	40	1600
	65	30	900
	70	35	1225
Mean	70	ss	10500

Variance of group 2:

Group 3: (Libertarians)

	Libertarians	deviation	squared deviation
	15	-20	400
	25	-10	100
	35	0	0
	40	5	25
	35	0	0
	25	-10	100
	45	10	100
	35	0	0
Mean	31.875	ss	725

Variance of group 3:

Number of observations in each group is 8. i.e. n = 8

Total number of groups is 3. i.e. k = 8

Total number of observations are 24. i.e. N = 24

Therefore,

Find grand mean:

Group mean	Grand mean	deviation	squared deviation
35	44.5833	-9.5833	91.83963889
70	44.5833	25.4167	646.0086389
31.875	44.5833	-12.7083	161.5008889
		SS	899.3491667

Test statistic:

df of test statistic is (k-1, N-k)

Thus here df is (2, 21)

p-value for is 0.0075.

p-value < 0.05

Hence we reject null hypothesis.

Thus we conclude that mean scale level for all three gropus is not equal. That means political party affiliation (democrat, republican, libertarian) likely to have an effect on how people feel about the war in Afghanistan.

APA writeup:

df = (2, 21), p-value = 0.0075

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