This is a continuation of Exercise 27 in Chapter 12. Kohler (1994, p. 427) reported data on the approval rates and ethnicity for mortgage appli­cants in Los Angeles in 1990. Of the 4096 African American applicants, 3117 were approved. Of the 84,947 white applicants, 71,950 were approved. The chi-square statistic for these data is about 220, so the difference observed in the approval rates is clearly statistically significant. Now suppose that a random sample of 890 applicants had been exam­ined, a sample size 100 times smaller than the one reported. Further, suppose the pattern of results had been almost identical, resulting in 40 African American applicants with 30 approved, and 850 white applicants with 720 approved.
a. Construct a contingency table for these numbers.
b. Compute the chi-square statistic for the table.
c. Make a conclusion based on your result in part (b), and compare it with the conclusion that would have been made using the full data set. Explain any discrepancies, and discuss their implications for this type of problem.