Question: 20. The chi-squared statistic for the data in Exercise 19 is about 220, so the differences observed in the approval rates are clearly statistically significant.

20. The chi-squared statistic for the data in Exercise 19 is about 220, so the differences observed in the approval rates are 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-squared 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.

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