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11-6 CONFIDENCE INTERVALS
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of the claim that if you can decrease the opponent s rushing yardage by 100 yards the team will win one more game 11-21. Consider the data from Exercise 11-5 on y sales price and x taxes paid. (a) Test H0: 1 0 using the t-test; use 0.05. (b) Test H0: 1 0 using the analysis of variance with 0.05. Discuss the relationship of this test to the test from part (a). (c) Estimate the standard errors of the slope and intercept. (d) Test the hypothesis that 0 0. 11-22. Consider the data from Exercise 11-6 on y steam usage and x average temperature. (a) Test for signi cance of regression using 0.01. What is the P-value for this test State the conclusions that result from this test. (b) Estimate the standard errors of the slope and intercept. (c) Test the hypothesis H0: 1 10 versus H1: 1 10 using 0.01. Find the P-value for this test. (d) Test H0: 0 0 versus H1: 0 0 using 0.01. Find the P-value for this test and draw conclusions. 11-23. Exercise 11-7 gave 20 observations on y highway gasoline mileage and x engine displacement. (a) Test for signi cance of regression using 0.01. Find the P-value for this test. What conclusions can you reach (b) Estimate the standard errors of the slope and intercept. (c) Test H0: 1 0.05 versus H1: 1 0.05 using 0.01 and draw conclusions. What is the P-value for this test (d) Test the hypothesis H0: 0 0 versus H1: 0 0 using 0.01. What is the P-value for this test 11-24. Exercise 11-8 gave 13 observations on y green liquor Na2S concentration and x production in a paper mill. (a) Test for signi cance of regression using 0.05. Find the P-value for this test. (b) Estimate the standard errors of the slope and intercept. (c) Test H0: 0 0 versus H1: 0 0 using 0.05. What is the P-value for this test 11-25. Exercise 11-9 presented data on y blood pressure rise and x sound pressure level. (a) Test for signi cance of regression using 0.05. What is the P-value for this test (b) Estimate the standard errors of the slope and intercept. (c) Test H0: 0 0 versus H1: 0 0 using 0.05. Find the P-value for this test.
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11-26. Exercise 11-11 presented data on y chloride concentration in surface streams and x roadway area. (a) Test the hypothesis H0: 1 0 versus H1: 1 0 using the analysis of variance procedure with 0.01. (b) Find the P-value for the test in part (a). (c) Estimate the standard errors of 1 and 0. (d) Test H0: 0 0 versus H1: 0 0 using 0.01. What conclusions can you draw Does it seem that the model might be a better t to the data if the intercept were removed 11-27. Refer to Exercise 11-12, which gives 20 observations on y shear strength of a propellant and x propellant age. (a) Test for signi cance of regression with 0.01. Find the P-value for this test. (b) Estimate the standard errors of 0 and 1. (c) Test H0: 1 30 versus H1: 1 30 using 0.01. What is the P-value for this test (d) Test H0: 0 0 versus H1: 0 0 using 0.01. What is the P-value for this test (e) Test H0: 0 2500 versus H1: 0 2500 using 0.01. What is the P-value for this test 11-28. Suppose that each value of xi is multiplied by a positive constant a, and each value of yi is multiplied by another positive constant b. Show that the t-statistic for testing H0: 0 versus H1: 1 0 is unchanged in value. 1 11-29. Consider the no-intercept model Y x with the s NID(0, 2). The estimate of 2 is s2 n n 2 x 2 2 1n g i 1 1 yi 12 and V 1 2 g i 1 x 2. i i (a) Devise a test statistic for H0: 0 versus H1: 0. (b) Apply the test in (a) to the model from Exercise 11-17. 11-30. The type II error probability for the t-test for H0: 1 1,0 can be computed in a similar manner to the t-tests of 9. If the true value of 1 is 1, the value d 0 1,0 12 Sxx is calculated and used as 1 0 1 11n the horizontal scale factor on the operating characteristic curves for the t-test, (Appendix Charts VIe through VIh) and the type II error probability is read from the vertical scale using the curve for n 2 degrees of freedom. Apply this procedure to the football data of Exercise 11-4, using 2.4 and 0.005, where the hypotheses are H0: 1 0.01 ver1 sus H1: 1 0.01.
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