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
12.2	8.1	20.9	17.8
9.6	17.3	16.4	8.6
10.7	19.7	22.6	14.3
8.1	10.4	5.6	21.2
16.8		19.9	19.7

(a) What is the level of significance?


(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
Between groups						.
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 95.989553 31.996518 1.1377173 0.3657 Error 15 421.8515 28.123433 Total 18 517.84105

SSTOT = 517.841

SSBT = 95.990

SSW = 421.852

dfBET = 3

dfW = 15

MSBET = 32.000

MSW = 28.123

F statistic = 1.138

(numerator) = 3
(denominator) = 15