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 ICountry IICountry IIICountry IV12.98.820.617.79.817.916.88.710.719.822.614.18.510.35.821.716.9 19.319.5(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? Make a summary table for your ANOVA test.

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Asked Dec 16, 2019
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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
12.9 8.8 20.6 17.7
9.8 17.9 16.8 8.7
10.7 19.8 22.6 14.1
8.5 10.3 5.8 21.7
16.9   19.3 19.5

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

SSTOT =  
SSBET =  
SSW =  


Find d.f.BETd.f.WMSBET, 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?

 

Make a summary table for your ANOVA test.

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Expert Answer

Step 1

Null Hypothesis:

H0: The mean earnings of immigrants for the four different countries are the same.

Alternative Hypothesis:

H1: At least one mean earning is different.

Procedure to obtain the values using MegaStat:

  • Enter the data in an excel sheet.
  • Go to MegaStat > Analysis of variance ...
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One factor ANOVA n Std. Dev Mean 9.97 5.288 Group 1 7.220 Group 2 11.76 8.233 Group 3 14.68 6.795 Group 4 14.28 12.71 23 6.762 Total ANOVA table p-value 6190 Source SS df MS Between Groups Within Groups 87.884 29.295 0.606 918.022 19 48.317 ........... Total 1,005.906 22

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