Crosstown busing to compensate for de facto segregation was begun on a fairly large scale in Nashville during the 1960s. Progress was made, but critics argued that too many racial imbalances were left unaddressed. Among the data cited in the early 1970s are the following figures, showing the percentages of African-American students enrolled in a random sample of eighteen public schools (165). Nine of the schools were located in predominantly African-American neighborhoods; the other nine, in predominantly white neighborhoods. Which version of the two-sample t test, Theorem 9.2.2 or the Behrens–Fisher approximation given in Theorem 9.2.3, would be more appropriate for deciding whether the difference between 35.9% and 19.7% is statistically significant? Justify your answer.
Schools in African-American Schools in White
Neighborhoods Neighborhoods
36%................................................. 21%
28…………………………………. 14
41…………………………………. 11
32…………………………………. 30
46…………………………………. 29
39…………………………………. 6
24…………………………………. 18
32…………………………………. 25
45…………………………………. 23
Average: 35.9%............................... Average: 19.7%