Practice Problems of Chapter 9, 10 and 11 1. A number of fetal stem cells may cross the placenta from the fetus to the mother during pregnancy and remain in the mother's tissue for decades. A recent study shows that the presence of fetal cells in the mother may offer some protection against the onset of breast cancer. Of the 54 women in the study with breast cancer, 14 had fetal cells. Of the 45 women without breast cancer, 25 had fetal cells. Test the claim that the population proportions of women with fetal cells is lower among women with breast cancer compared to women without breast cancer, using level of significance = 0.01. Assume the requirements are met. Use the critical value method and the P-value method of testing hypotheses. (Section 9.2) 2. The American Federation of Teachers publishes an annual teacher salary report. In 2003, California led the nation in mean teacher salary with $55,693, with Michigan in second place with $54,020. Suppose the data are from random samples of size 100 each, with a standard deviation of $10,000 in California and $9,000 in Michigan. Test at level of significance = 0.05 whether the population mean salary in California is greater than in Michigan. Verify the requirements of testing the claim. Use the critical value method and the P-value method of testing hypotheses. (Section 9.3) 3. A researcher claims that listening to Mozart improves scores on math quizzes. A random sample of five students took math quizzes, first before and then after listening to Mozart. Perform the hypotheses test for determining whether the results support the researcher's claim, using level of significance =0.10. Verify the requirements of testing the claim. Use the critical value and the P-value method of testing hypotheses. (Section 9.4) Students 1 2 3 4 5 Before 75 50 80 85 95 After 85 45 85 95 95 4. Listed below are heights (in inches) and weights (in pounds) for nine random supermodels. Is there a correlation between height and weight? If there is a correction, does it mean that there is a correlation between height and weight of all adult women? Assume the requirements are met. Use the critical value method and the P-value method of testing hypotheses. (Section 10.2) Height (in.) 71 Weight 125 (in.) 70.5 71 72 70 70 66.5 70 71 119 128 128 119 127 105 123 115 5. The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. All of the diamonds are round with ratings of \"very good\" cut, they all have a color rating of F (\"slight color\"), and a clarity rating of VSI (\"very slightly included\"). The values are based on data from the retailer Blue Nile. Not included in the table below is a diamond with a weight of 1.50 carats. Find the regression equation, and then find best predicted price of this diamond. Is the result close to the actual price of $16,097? What is wrong with predicting the price of a 1.50-carat diamond? (Section 10.3) Weight 0.3 0.4 0.5 0.5 1.0 0.7 Price 510 1151 1343 1410 5669 2277 6. The author drilled a hole in a die and filled it with a lead weight, then proceed to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 31, 42, 40, 28, 32. Use a 0.05 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? Assume all requirements are met. Use critical value method of testing hypotheses. (Section 11.2) 7. The U.S. Supreme Court considered a case involving the exam for firefighter lieutenant in the city of New Haven, Connecticut. Results from the exam are shown in the table below. Is there sufficient evidence to support the claim that results from the test should be thrown out because they are discriminatory? Use a 0.01 significance level. Assume all requirements are met. Use critical value of testing hypotheses. (Section 11.3) Passed Failed White Candidates 17 16 Minority Candidates 9 25