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Chapter 10: Problem 2
In Chapter 9 , you learned some tests of means. Are tests of means used for numerical or categorical data?
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One treatment for multiple myeloma (cancer of the blood and bones) is a stem cell transplant. However, in some cases the cancer returns. McCarthy and colleagues reported on a study that randomly assigned 460 patients ( 100 days after a stem cell transplant) to receive either lenalidomide or placebo. At one point in the study, 46 of the patients who received the real drug had a bad result (had progressive disease or had died), compared to 101 of those who received the placebo. Assume that exactly half were assigned to each group. a. Find and compare the percentages that had a bad result for the two groups. b. Test the hypothesis that the drug reduced the chance of a bad result compared to the placebo using a significance level of \(0.05\). c. The study started in April 2005 and was "unblinded" in 2009 when an interim analysis showed better results with the group taking the drug. After the unblinding, many of the patients from the placebo group "crossed over" to the drug group. Explain what you think "unblinding" means and why this seems like a reasonable thing to do. (Source: P. L. McCarthy et al. 2012. Lenalidomide after stem-cell transplantation for multiple myeloma. New England Journal of Medicine 366, 1770-1781.)
In Montreal, Canada, an experiment was done with parents of children who were thought to have a high risk of committing crimes when they became teenagers. Some of the families were randomly assigned to receive parental training, and the others were not. Out of 43 children whose parents were randomly assigned to the parental training group, 6 had been arrested by the age of \(15 .\) Out of 123 children whose parents were not in the parental training group, 37 had been arrested by age 15 . a. Find and compare the percentages of children arrested by age \(15 .\) Is this what researchers might have hoped? b. Create a two-way table from the data, and test whether the treatment program is associated with arrests. Use a significance level of \(0.05\). c. Do a two-proportion \(z\) -test, testing whether the parental training lowers the rate of bad results. Use a significance level of \(0.05\). d. Explain the difference in the results of the chi-square test and the two- proportion z-test. e. Can you conclude that the treatment causes the better result? Why or why not?
The Perry Preschool Project discussed in Exercises \(10.23-10.25\) found that 8 of the 58 students who attended preschool had at least one felony arrest by age 40 and that 31 of the 65 students who did not attend preschool had at least one felony arrest (Schweinhart et al. 2005). a. Compare the percentages descriptively. What does this comparison suggest? b. Create a two-way table from the data and do a chi-square test on it, using a significance level of \(0.05 .\) Test the hypothesis that preschool attendance is associated with being arrested. c. Do a two-proportion \(z\) -test. Your alternative hypothesis should be that preschool attendance lowers the chances of arrest. d. What advantage does the two-proportion \(z\) -test have over the chisquare test?
School Dropout Rates The school dropout rate in an Indian village is about \(25 \%\), which means that \(25 \%\) of the students leave school without completing their education. There have been many attempts to reduce this rate. One of these attempts is to encourage students to restart education through incentives like midday meals and financial assistance. Suppose you want to determine whether the encouragement methods actually help in reducing the dropout rate. Suppose that students who are aided with incentives are observed for a year to see whether they drop out. a. Describe a study based on a sample of students that would allow the management to conclude that encouragement causes a reduction in dropout rate but would not allow it to generalize this result to students in all villages. b. Describe a study based on a sample of students that does not allow the management to conclude that encouragement causes a reduction in dropout rate but does allow it to generalize to students in all villages. c. Describe a study based on a sample of students that allows the management to conclude that encouragement causes a reduction in the dropout rate and also allows it to generalize to students in all villages.
Tests a. In Chapter 8 , you learned some tests of proportions. Are tests of proportions used for categorical or numerical data? b. In this chapter, you are learning to use chi-square tests. Do these tests apply to categorical or numerical data?
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