Question 20.18

A large study of child care used samples from the data tapes of 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, non-household, and preschool teacher. Here are data on the number of blacks among women workers in these three classes:

Total Black

Household 2455 172

Non-household 1191 167

Teachers 659 86

1. What percent of each class of child-care workers is black?
2. Make a two-way table of class of worker by race (black or other)
3. Can we safely use the chi-square test? What null and alternative hypotheses does X ² test?
4. The chi-square test for this table is X ² = 53.194. What are its degrees of freedom? Use table E to approximate the P value.
5. What do you conclude from these data?

Question 20.28

Cancer of the colon and rectum is common in the Mediterranean region than in other Western countries. The Mediterranean diet contains little animal fat and lots of olive oil. Italian researchers compared 1953 patients with colon or rectal cancer with a control group of 4154 patients admitted to the same hospitals for unrelated reasons. They estimated consumption of various foods from a detailed interview, then divided the patients into three groups according to their consumption of olive oil. Here are some of the data.

1. Is this study an experiment? Explain your answer
2. Is high olive oil consumption more common among patients without cancer than in patients with colon cancer or rectal cancer?
3. Find the chi-square statistic X ² What would be the mean of X ² if the null hypothesis (no relationship) were true? What does comparing the observed value of X ² with this mean suggest? What is the P value? What do you conclude?
4. The investigators report that "less than 4% of cases or controls refused to participate." Why does this fact strengthen our confidence in the results?

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