A local politician is concerned that a program for the homeless in the city is discriminating against blacks and other minorities. The following data were taken from a random sample of black and white homeless people. Race Receive d Services yes no Black 6 4 White 7 9 13 13 10 16 26 a. Is there a statistically significant relationship between race and whether the person received services from the program? b. Compute column or row percentage for the table to determine the pattern of the relationship. Which group was more likely to receive services in the sample? Interpret the percentages that you have obtained. SAMPLE RESPONSE Part 2. Chi-square test Assumptions 1. 2. Our samples are random and independent. Level of measurement of both variables is nominal. Hypotheses Research: Salary depends on unionization in the population. Null: Salary and unionization are independent in the population. Chi-critical. d.f. (2-1)*(2-1) = 1. Chi critical = 3.841 Expected frequencies (fe): For top left cell: fe (50)(35) 1750 17.50 100 100 fe (50)(65) 3250 32.50 100 100 fe (50)(35) 1750 17.50 100 100 fe (50)(65) 3250 32.50 100 100 For top right cell: For bottom left cell: For bottom right cell: Step 4. Computing the test statistic fo 21 29 14 36 N = 100 fe 17.50 32.50 17.50 32.50 N = 100 fo - fe 3.50 -3.50 -3.50 3.50 0.00 (fo - fe)2 12.25 12.25 12.25 12.25 (fo - fe)2 / fe 0.70 0.38 0.70 0.38 2(obtained) = 2.16 2(obtained) = 2.16 Chi critical: D.F. =1 .05 alpha Chi critical = 3.841 Conclusion: We fail to reject the Null. Unionization and salary are not related. They are independent in the population