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6-34. Construct a frequency distribution and histogram with 16 bins for the motor fuel octane data in Exercise 6-14. Compare its shape with that of the histogram with eight bins from Exercise 6-30. Do both histograms display similar information 6-35. Construct a histogram for the female student height data in Exercise 6-22. 6-36. Construct a histogram with 10 bins for the spot weld shear strength data in Exercise 6-23. Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf display 6-37. Construct a histogram for the water quality data in Exercise 6-24. Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf display 6-38. Construct a histogram with 10 bins for the overall distance data in Exercise 6-25. Comment on the shape of the histogram. Does it convey the same information as the stem-andleaf display 6-39. Construct a histogram for the semiconductor speed data in Exercise 6-26. Comment on the shape of the his-

Raw Materials (arguments) Factory (function) Product (return value)

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togram. Does it convey the same information as the stem-andleaf display 6-40. Construct a histogram for the pinot noir wine rating data in Exercise 6-27. Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf display 6-41. The Pareto Chart. An important variation of a histogram for categorical data is the Pareto chart. This chart is widely used in quality improvement efforts, and the categories usually represent different types of defects, failure modes, or product/process problems. The categories are ordered so that the category with the largest frequency is on the left, followed by the category with the second largest frequency and so forth. These charts are named after the Italian economist V Pareto, . and they usually exhibit Pareto s law ; that is, most of the defects can be accounted for by only a few categories. Suppose that the following information on structural defects in automobile doors is obtained: dents, 4; pits, 4; parts assembled out of sequence, 6; parts undertrimmed, 21; missing holes/slots, 8; parts not lubricated, 5; parts out of contour, 30; and parts not deburred, 3. Construct and interpret a Pareto chart.

We are interested in testing H0: 0 against the usual alternatives. Assume that X1, X2, . . . , Xn is a random sample from a continuous and symmetric distribution with mean (and median) . Compute the differences Xi 1, 2, . . . , n. Rank the absolute differences 0, i 0 Xi 1, 2, . . . , n in ascending order, and then give the ranks the signs of their 00,i corresponding differences. Let W be the sum of the positive ranks and W be the absolute value of the sum of the negative ranks, and let W min(W , W ). Appendix Table VIII contains critical values of W, say w*. If the alternative hypothesis is H1: 0 , then if the observed value of the statistic w w*, the null hypothesis H0: 0 is rejected. Appendix Table VIII provides signi cance levels of 0.10, 0.05, 0.02, 0.01 for the two-sided test. w*; and if For one-sided tests, if the alternative is H1: 0, reject H0: 0 if w the alternative is H1: w*. The signi cance levels for one0, reject H0: 0 if w sided tests provided in Appendix Table VIII are 0.05, 0.025, 0.01, and 0.005.

In its simplest form, a return statement is the keyword return followed by the value that you want to return. This value can be a literal, a variable, the result of another function, or any other type of expression.

EXAMPLE 15-4

message log pane for that node, changing the color of the node in the display, drawing a circle around the node to indicate some node state of interest, etc. The information sent as part of a GUIMessage is shown in the code listing of Figure 4.17. Additional message types and their associated variables can be easily defined by adding the corresponding code to this class.

return someValue;

We will illustrate the Wilcoxon signed-rank test by applying it to the propellant shear strength data from Table 15-1. Assume that the underlying distribution is a continuous symmetric distribution. The eight-step procedure is applied as follows: The parameter of interest is the mean (or median) of the distribution of propellant shear strength. 2. H0: 2000 psi 3. H1: 2000 psi 4. 0.05 5. The test statistic is 1. w min1w , w 2

Notice that no parentheses are used in conjunction with the return statement. This is because it is an operator, not a function. You may see parentheses used sometimes, as in return (someValue), but they are not required. In this case the purpose of the parentheses is not to invoke a function but to group an expression, as in (1+2)*3. In most situations, you ll want to manipulate the arguments within your function somehow and then return a new calculated value. This example calculates the circumference of a circle by taking a single variable, diameter, multiplying it by the mathematical constant , and returning the result as a number:

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