The National Association of Home Builders provided data on the cost of the most popular home remodeling projects. Sample data on cost in thousands of dollars for two types of remodeling projects are contained in the file Remodeling.xlsx. We wish to compare the population mean remodeling costs for the two types of projects based on a significance level =0.05 =0.05 and assuming that both populations have a normal distribution. Hint: Refer to Section 10.2 to help answer this question. (1) State the hypotheses. (2) Use XLSTAT to compute the test statistic and the p-value. Hint: Select Parametric tests > Two-sample t-test and z-test. Select cells A1:A11 for Sample 1, select cells B1:B9 for Sample 2, and select Students t . (3) What is your hypothesis test decision? Hint: There are two possible decisions: reject H0 in favour of Ha or fail to reject H0. (4) What is your conclusion in the context of the application? Hint: The conclusion should relate back to the question. (5) Suppose we are not willing to assume that both populations have a normal distribution. Then, we should not use a parametric two-sample t-test, but we can instead use a nonparametric Mann-Whitney-Wilcoxon test for the difference in the population median remodeling costs for the two types of projects. Use XLSTAT to compute the z test statistic and the p-value. Are they similar to the corresponding values you obtained in part (b)?

2. The College Board SAT college entrance test consists of three parts: math, writing, and critical reading (The World Almanac, 2012). Sample data showing the math and writing scores for a sample of 12 students who took the SAT are contained in the file TestScores.xlsx. Note that each student has both a math score and a writing score, so this is a matched sample design. We wish to compare the population mean math and writing scores based on a significance level =0.05 =0.05 and assuming that the differences between the paired observations are normally distributed. Hint: Refer to Section 10.3 to help answer this question. (1) State the hypotheses. (2) Calculate the differences (math score writing score) for each student in column D of the Excel spreadsheet, and then use XLSTAT to compute the test statistic and the p-value. Hint: Select Parametric tests > One-sample t-test and z-test. Select cells D1:D13 for the Data, and select Students t test. Click Options and select Mean 1 Theoretical mean and type 0 for the theoretical mean. (3) What is your hypothesis test decision? Hint: There are two possible decisions: reject H0 in favour of Ha or fail to reject H0. (4) What is your conclusion in the context of the application? Hint: The conclusion should relate back to the question. (5) Suppose we are not willing to assume that the differences between the paired observations are normally distributed. Then, we should not use a parametric one-sample t-test, but we can instead use a nonparametric Wilcoxon signed-rank test for the difference in the population median math and writing scores. Use XLSTAT to compute the z test statistic and the p-value. Are they similar to the corresponding values you obtained in part (b)?

3. Medical tests were conducted to learn about drug-resistant tuberculosis. Of 142 cases tested in British Columbia, 9 were found to be drug resistant. Of 268 cases tested in Ontario, 5 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two provinces? Use a significance level =0.01 =0.01 . Hint: Refer to Section 10.4 to help answer this question. (1) State the hypotheses. (2) Calculate the test statistic. (3) Use Excel to find the p-value. Hint: Use NORM.DIST. (4) What is your hypothesis test decision? Hint: There are two possible decisions: reject H0 in favour of Ha or fail to reject H0. (5) What is your conclusion in the context of the application? Hint: The conclusion should relate back to the question.