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conclusions can you draw about the difference in mean mileage performance for the two vehicles in this study 15-52. Use the large-sample approximation for the Wilcoxon rank-sum test for the fuel-economy data in Exercise 10-83. What conclusions can you draw about the difference in means if 0.01 Find the P-value for this test. 15-53. Use the Wilcoxon rank-sum test with 0.025 for the ll-capability experiment described in Exercise 10-85. What conclusions can you draw about the capability of the two llers 15-54. Use the large-sample approximation for the Wilcoxon rank-sum test with 0.025 for the ll-capability experiment described in Exercise 10-85. Find the P-value for this test. What conclusions can you draw 15-55. Consider the contact resistance experiment in Exercise 13-31. Use the Kruskal-Wallis test to test for differences in mean contact resistance among the three alloys. If 0.01, what are your conclusions Find the P-value for this test. 15-56. Consider the experiment described in Exercise 13-28. Use the Kruskal-Wallis test for this experiment with 0.05. What conclusions would you draw Find the P-value for this test. 15-57. Consider the bread quality experiment in Exercise 13-35. Use the Kruskal-Wallis test with 0.01 to analyze the data from this experiment. Find the P-value for this test. What conclusions can you draw

So pixels where the neighbors are of different brightness are enhanced, which appears to sharpen the image The cMat matrix produces a simple Gaussian blur, much like a BlurFilter can provide A Gaussian blur averages neighboring pixels within a given radius To blur more or less, you would create matrices of the same form with greater or smaller sizes A larger matrix takes into account pixels farther away, thus increasing the radius or blurriness of the blur Note that rather than set each coef cient to 1/9, I ve written in all the coef cients as 1 and used a divisor of 9 This saved me some typing Finally, dMat produces a cheesy-looking emboss.

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15-58 For the large-sample approximation to the Wilcoxon signed-rank test, derive the mean and standard deviation of the test statistic used in the procedure 15-59 Testing for Trends A turbocharger wheel is manufactured using an investment-casting process The shaft ts into the wheel opening, and this wheel opening is a critical dimension As wheel wax patterns are formed, the hard tool producing the wax patterns wears This may cause growth in the wheel-opening dimension Ten wheel-opening measurements, in time order of production, are 400 (millimeters), 402, 403, 401, 400, 403, 404, 402, 403, 403 (a) Suppose that p is the probability that observation Xi 5 exceeds observation Xi If there is no upward or downward trend, Xi 5 is no more or less likely to exceed Xi or lie below Xi.

What is the value of p (b) Let V be the number of values of i for which Xi 5 Xi If there is no upward or downward trend in the measurements, what is the probability distribution of V (c) Use the data above and the results of parts (a) and (b) to test H0: there is no trend, versus H1: there is upward trend Use 005 Note that this test is a modi cation of the sign test It was developed by Cox and Stuart 15-60 Consider the Wilcoxon signed-rank test, and suppose that n 5 Assume that H0: 0 is true (a) How many different sequences of signed ranks are possible Enumerate these sequences (b) How many different values of W are there Find the probability associated with each value of W .

By inversely removing contributions from the upper-left quadrant of neighbors and adding contributions from the bottom-right quadrant of neighbors, you emphasize pixels where the contrast is high in one direction, as if they are lit up by light coming from that direction in this case, a diagonal from bottom right to top left So that you can look at the results in more detail, holding down the mouse button on any of the images scales the image up temporarily These lters, and others you can perform with a convolution lter, may not be high quality, but they are excellent for preparing images and video for analysis by computer vision algorithms They run fast and can emphasize certain local features of images that may be important..

(c) Suppose that we de ne the critical region of the test to be to reject H0 if w w* and w* 13 What is the approximate level of this test (d) Does this exercise show how the critical values for the Wilcoxon signed-rank test were developed Explain..

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