Question

5.48 Work hours and education: The General Social Survey collects data on demographics, education, and work, among many other characteristics of US residents. Using ANOVA, we can consider educational attainment levels for all 1,172 respondents at once. Below are the distributions of hours worked by educational attainment and relevant summary statistics that will be helpful in carrying out t his analysis.

Answer 1

n = Total number of respondents = 1172

number of groups ( Educantion attainment ) = 5

a ) In Anova

we test the hypothesis that

Ho : All the groups having same mean

against

H1 : Atleast one of the mean is different.

Here number of groups = 5

Correct option

A: Ho .mu1=mu2=mu3=mu4=m5

Ha : At least of the mean is different.

b) Anova table

	D.F	S.S	M.S.S	F-value	Pr(>F)
degree (Groups)	4	2006.16	501.54	2.1889	0.0682
reisduals (error)	1167	267382	222.1191	-------------
Total	1171	269388.16	---------	-------------

i) D.F.

The number of groups =5

D.F. for groups =5-1 = 4

The total number of respondent = 1172

D.F. for total =1172-1 =1171

D.F. for residual = 1171 - 4 = 1167

ii) S.S.

Since M.S.S. = S.S / D.F

S.S. for degree = 4 * 501.54 = 2006.16

S.S. for total = S.S. for residual + S.S . for degree = 2006.16 + 267382 = 269388.16

iii) M.S.S.

M.S.S. = S.S /D.F

M.S.S. for residuals = S.S. for residuals / D.F. = 267382/ 1167 = 229.1191

iv) F-value = M.S. for degree / M.S. for residuals = 501.54 / 222.1191 = 2.1889

c) Value of test statistics =F-value =2.188

d) p-value= P(>F) = 0.0682

e) alpha =level of significance =0.05

Since p-value > alpha

Interpretation :

Since p>= alpha we accept the null hypothesis that all groups work the same average number of hours per week.