Question

A researcher was curious about whether people’s attitudes are related to their behaviors. As a simple experiment, the researcher measured people’s attitudes and behaviors regarding housework.

On the attitude side, the researcher measured the level of agreement on the statement “It is much better for everyone involved in housework: strongly agree, agree, disagree, and strongly disagree” On the behavioral side, the respondents are asked to estimate how many hours of housework they do per week.

Based on your analysis of the data below, please come up with a conclusion whether people who respond differently to the attitudinal question actually behave differently?

Once you have arrived at an answer to each question, please write a sentence or two interpreting the result (100 pts).

Attitude	Strongly Agree	Agree	Disagree	Strongly Disagree
	34	28	40	43
	31	26	42	42
	33	24	39	38
	32	26	32	39
	28	32	41	41
	27	34	39	44
	43	27	43	48
	38	26	44	36
	27	31	41
	31		39
Sample N	10	9	10	8
Sample Mean	32.40	28.22	40.00	41.38
Sample St.Dev	5.03	3.35	3.30	3.78

1. State the null and alternative hypotheses. (15 pts)
2. Find the critical value from the F test distribution. (15 pts)
3. ANOVA computation (Mean and Variance of each sample groups were provided with the data.

c.1. Find the grand mean, the mean of all values in the samples. (10 pts)

c.2. Find the between-group variance. (15 pts)

c3. Find the within group variance.

c.4. Compute the F-value. (15 pts)

4. At α = 0.05, can it be concluded that there is a significant difference in the behavior among the groups with different attitudes toward housework? Why or why not? Make the decision and summarize the results. (15 pts)

Answer 1

Ans a ) the null ad alternative hypothesis is

Ho:u1=u2=u3=u4

Ha: at least one u is different

using excel>data >data analysis>one way anova

we have

SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	10	324	32.4	25.37778
Column 2	9	254	28.22222	11.19444
Column 3	10	400	40	10.88889
Column 4	8	331	41.375	14.26786
		grand mean	35.499
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1050.872	3	350.2907	22.40967	4.26E-08	2.891564
Within Groups	515.8306	33	15.63123
Total	1566.703	36

Ans b )  the critical value from the F test distribution is 2.892

c.1.the grand mean, the mean of all values in the samples. is 35.499

c.2 the between-group variance from table is 350.2907

c3 the within-group variance from table is 15.631

c.4. the F-value = 22.41

1. At α = 0.05, we cannot concluded that there is a significant difference in the behavior among the groups with different attitudes toward housework because f stat > f critical value or p value of f statistic is less than 0.05  \