Question

A sociologist studying New York City ethnic groups wants to determine if there is a difference in income for immigrants from four different countries during their first year in the city. She obtained the data in the following table from a random sample of immigrants from these countries (incomes in thousands of dollars). Use a 0.05 level of significance to test the claim that there is no difference in the earnings of immigrants from the four different countries.

Country I	Country II	Country III	Country IV
12.1	8.3	20.7	17.9
9.3	17.2	16.2	8.3
10.8	19.7	22.8	14.7
8.3	10.2	5.8	21.5
16.5		19.2	19.4

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Round your answers to three decimal places.)

SSTOT	=
SSBET	=
SSW	=

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Round your answer to three decimal places for MS_BET and MS_W.)

dfBET	=
dfW	=
MSBET	=
MSW	=

Find the value of the sample F statistic. (Round your answer to three decimal places.)


What are the degrees of freedom?

	(numerator)
	(denominator)

(c) Find the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100     0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001

(f) Make a summary table for your ANOVA test.

Source of Variation	Sum of Squares	Degrees of Freedom	MS	F Ratio	P Value	Test Decision
Between groups					---Select--- p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001	---Select--- Do not reject H0. Reject H0.
Within groups
Total

Answer 1

b)

SSTOT	=	510.632
SSBET	=	96.198
SSW	=	414.434

dfBET	=	3
dfW	=	15
MSBET	=	32.066
MSW	=	27.629

value of the sample F statistic =1.161

degrees of freedom (numerator)=3

degrees of freedom (Denominator)=15

c)

P-value > 0.100

f)

Source of Variation	SS	df	MS	F	P-value	test devision
Between Groups	96.198	3	32.066	1.161	0.3574	Do not reject Ho
Within Groups	414.434	15	27.629
Total	510.632	18