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S5-25. The photoresist thickness in semiconductor manufacturing has a mean of 10 micrometers and a standard deviation of 1 micrometer. Bound the probability that the thickness is less than 6 or greater than 14 micrometers. S5-26. Suppose X has a continuous uniform distribution with range 0 x 10. Use Chebyshev s rule to bound the probability that X differs from its mean by more than two standard deviations and compare to the actual probability. S5-27. Suppose X has an exponential distribution with mean 20. Use Chebyshev s rule to bound the probability that X differs from its mean by more than two standard deviations and by more than three standard deviations and compare to the actual probabilities. S5-28. Suppose X has a Poisson distribution with mean 4. Use Chebyshev s rule to bound the probability that X differs from its mean by more than two standard deviations and by more than three standard deviations and compare to the actual probabilities. S5-29. Consider the process of drilling holes in printed circuits boards. Assume that the standard deviation of the diameters is 0.01 and that the diameters are independent. Suppose that the average of 500 diameters is used to estimate the process mean. (a) The probability is at least 15 16 that the measured average is within some bound of the process mean. What is the bound (b) If it is assumed that the diameters are normally distributed, determine the bound such that the probability is 15 16 that the measured average is closer to the process mean than the bound. S5-30. Prove Chebyshev s rule from the following steps. De ne the random variable Y as follows: Y (a) (b) (c) (d) e 1 0 if 0 X 0 otherwise c

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 005 (b) Test H0: 1 0 using the analysis of variance with 005 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 001 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.

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(c) Test the hypothesis H0: 1 10 versus H1: 1 10 using 001 Find the P-value for this test (d) Test H0: 0 0 versus H1: 0 0 using 001 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 001 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: 1 005 versus H1: 1 005 using 001 and draw conclusions What is the P-value for this test (d) Test the hypothesis H0: 0 0 versus H1: 0 0 using 001 What is the P-value for this test 11-24.

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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 005 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 005 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 005 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 005 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 001 (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 001 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 001 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 001.

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