Question

A sociologist studying New York City ethnic groups wants to determine if there is a difference...

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 SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Round your answers to three decimal places.)

SSTOT =
SSBET =
SSW =


Find d.f.BET, d.f.W, MSBET, and MSW. (Round your answer to three decimal places for MSBET and MSW.)

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

Homework Answers

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
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