508 CHAPTER 9 Correlation and Regression Extending Concepts Hypothesis Testing for Slope When testing the slope M of the regression line for the population, you usually test that the slope is 0, or H0: M= 0. A slope of 0 indicates that there is no linear relationship between x and y. To perform the t-test for the slope M, use the standardized test statistic t = m se B Σx2 - 1Σx22 n with n - 2 degrees of freedom. Then, using the critical values found in Table 5 in Appendix B, make a decision whether to reject or fail to reject the null hypothesis. You can also use the LinRegTTest feature on a TI-84 Plus to calculate the standardized test statistic as well as the corresponding P-value. If P … a, then reject the null hypothesis. If P 7 a, then do not reject H0. In Exercises 35 and 36, test the claim and interpret the results in the context of the problem. If convenient, use technology. 35. The table shows the weights (in pounds) and the numbers of hours slept in a day by a random sample of infants. Test the claim that M≠ 0. Use a = 0.01. Weight, x 8.1 10.2 9.9 7.2 6.9 11.2 11 15 Hours slept, y 14.8 14.6 14.1 14.2 13.8 13.2 13.9 12.5 36. The table shows the ages (in years) and salaries (in thousands of dollars) of a random sample of employees at a company. Test the claim that M≠ 0. Use a = 0.05. Age, x 25 34 29 30 42 38 49 52 35 40 Salary, y 57.5 61.2 59.9 58.7 87.5 67.4 89.2 85.3 69.5 75.1 Confidence Intervals for y-Intercept and Slope You can construct confidence intervals for the y-intercept B and slope M of the regression line y = Mx + B for the population by using the inequalities below. y-intercept B: b - E 6 B 6 b + E where E = tcseR 1 n + x2 Σx2 - 1Σx22 n and slope M: m - E 6 M6 m + E where E = tcse B Σx2 - 1Σx22 n The values of m and b are obtained from the sample data, and the critical value tc is found using Table 5 in Appendix B with n - 2 degrees of freedom. In Exercises 37 and 38, construct the indicated confidence intervals for B and M using the gross domestic products and carbon dioxide emissions data found in Example 2. 37. 95% confidence interval 38. 99% confidence interval
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