Introduction to Probability and Statistics for Engineers and Scientists
504 Chapter 11:Goodness of Fit Tests and Categorical Data Analysis Therefore, the hypothesis that the percentages of women who f ...
*11.6The Kolmogorov–Smirnov Goodness of Fit Test for Continuous Data 505 To compute the value ofDfor a given data setYj=yj,j=1,. ...
506 Chapter 11:Goodness of Fit Tests and Categorical Data Analysis Similarly, the maximum value ofF(x)−Fe(x) is also nonnegative ...
*11.6The Kolmogorov–Smirnov Goodness of Fit Test for Continuous Data 507 whereU 1 ,...,Unare independent uniform (0, 1) random v ...
508 Chapter 11:Goodness of Fit Tests and Categorical Data Analysis The levelαtest would reject the null hypothesis thatFis the d ...
Problems 509 Test the hypothesis that the die is fair (that is, thatpi=^16 ,i=1,...,6)atthe 5 percent level of significance. Use ...
510 Chapter 11:Goodness of Fit Tests and Categorical Data Analysis top grade 234 high grade 117 medium grade 81 low grade 68 Can ...
Problems 511 In a certain region, insurance data indicate that 82 percent of drivers have no accidents in a year, 15 percent ha ...
512 Chapter 11:Goodness of Fit Tests and Categorical Data Analysis Determine the p-value of the test that a family’s income and ...
Problems 513 Defective Acceptable Superior Before 25 218 22 After 9 103 14 Is this change significant at the .05 level? 21.A sam ...
514 Chapter 11:Goodness of Fit Tests and Categorical Data Analysis Test the hypothesis that the percentages of the surgical oper ...
Chapter 12 Nonparametric Hypothesis Tests............................ 12.1 Introduction In this chapter, we shall develop some h ...
516 Chapter 12:Nonparametric Hypothesis Tests This hypothesis can easily be tested by noting that each of the observations will, ...
12.2The Sign Test 517 The sign test can also be used in situations analogous to ones in which the paired t-test was previously a ...
518 Chapter 12:Nonparametric Hypothesis Tests area = 1/2 m area > 1/2 m m 0 area < 1/2 m 0 m FIGURE 12.1 resultingp-value ...
12.3The Signed Rank Test 519 wherepis the probability that a randomly chosen member of the population has an annual income of le ...
520 Chapter 12:Nonparametric Hypothesis Tests 1.0 0.8 0.6 0.4 0.2 0.0 1 x 0 23456 y FIGURE 12.2 A symmetric density: m= 3. f(x)= ...
12.3The Signed Rank Test 521 Var(T)=Var ∑n j= 1 jIj = ∑n j= 1 j^2 Var(Ij) = ∑n j= 1 j^2 4 = n(n+1)(2n+1) 24 (12.3.2) whe ...
522 Chapter 12:Nonparametric Hypothesis Tests where t∗=min ( t, n(n+1) 2 −t ) It remains to computePH 0 {T≤t∗}. To do so, letPk( ...
12.3The Signed Rank Test 523 we see that Pk(i)=^12 Pk− 1 (i−k)+^12 Pk− 1 (i) (12.3.6) Starting with Equation 12.3.5, the recursi ...
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