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
12.4	8.3	20.2	17.1
9.9	17.1	16.2	8.3
10.6	19.7	22.2	14.8
8.9	10.5	5.2	21.7
16.2		19.3	19.7

(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)

(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--- Reject H0. Do not reject H0.
Within groups
Total

Answer 1

The statistic software output for this problem is:

ANOVA table

Source	DF	SS	MS	F-Stat	P-value
Columns	3	82.111368	27.370456	1.0035218	0.4184
Error	15	409.116	27.2744
Total	18	491.22737

SSTOT = 491.227

SSBT = 82.111

SSW =409.1116

dfBET = 3

dfW = 15

MSBET = 27.370

MSW = 27.274

F statistic = 1.004

(numerator) = 3
(denominator) = 15