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 12.3 8.3 20.4 17.3 9.1 17.2 16.5 8.7 10.9 19.2 22.8 14.2 8.8 10.2 5.5 21.4 16.1 19.2 19.3 (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) 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
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 |
| 12.3 | 8.3 | 20.4 | 17.3 |
| 9.1 | 17.2 | 16.5 | 8.7 |
| 10.9 | 19.2 | 22.8 | 14.2 |
| 8.8 | 10.2 | 5.5 | 21.4 |
| 16.1 | 19.2 | 19.3 |
(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) |
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 |
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