A large study of child care used samples from the data tapes on the current population survey over a period of several years. The result is close to an SRS of child care workers. The current population survey has three classes of child care workers: private household, nonhousehold, and preschool teacher. Here are data on the number of blacks among women workers in these three classes:
Household 2455 172
Nonhousehold 1191 167
Teachers 659 86
a) What percent of each class of child care workers is black?
b) Make a two-way table of class of worker by race (black or other)
c) Can we safely use the chi-square test? what null and alternate hypothesis does X2(x squared) test?
d) The chi-square statistic for this table is X2(x squared)= 53.194. What are its degrees of freedom? What is the mean of X2(x squared) if the null hypothesis is true? Use the chi-square distribution critical values table to approximate the P-value of the test.
e) What do you conclude from these data?
This solution conducts a statistical analysis on classes of childcare workers by determining percentages of ethnicity, using chi-square tests and making conclusions about the data.