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barcode font reporting services Tests of Hypotheses and Significance in Software
CHAPTER 7 Tests of Hypotheses and Significance QR Code Recognizer In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Generating Denso QR Bar Code In None Using Barcode encoder for Software Control to generate, create QR image in Software applications. so that (3) (4) a1 n1P1, a2 n2P2, nA b1 np, n1(1 nB P1), nq b2 n2(1 P2) Scanning QRCode In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Printing QR Code In C# Using Barcode generator for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in .NET applications. Using (3) and (4), we have from Problem 7.49 x2 n(a1b2 a2b1)2 n1n2nAnB n1n2(P1 P2)2 npq n[n1P1n2(1 P2) n2P2n1(1 n1n2npnq (since n P1)]2 QR Code Printer In .NET Framework Using Barcode creation for ASP.NET Control to generate, create Denso QR Bar Code image in ASP.NET applications. QR Code 2d Barcode Generation In .NET Framework Using Barcode encoder for Visual Studio .NET Control to generate, create Denso QR Bar Code image in .NET applications. (P1 P2)2 pq(1>n1 1>n2) QR Generation In VB.NET Using Barcode generator for .NET Control to generate, create QR Code JIS X 0510 image in Visual Studio .NET applications. Generating Data Matrix 2d Barcode In None Using Barcode maker for Software Control to generate, create Data Matrix 2d barcode image in Software applications. which is the square of the Z statistic given in (10) on page 217.
UPC A Printer In None Using Barcode encoder for Software Control to generate, create UPCA image in Software applications. EAN13 Generator In None Using Barcode maker for Software Control to generate, create EAN 13 image in Software applications. Coefficient of contingency 7.52. Find the coefficient of contingency for the data in the contingency table of Problem 7.45. Creating Bar Code In None Using Barcode creator for Software Control to generate, create bar code image in Software applications. GTIN  128 Maker In None Using Barcode encoder for Software Control to generate, create UCC  12 image in Software applications. C x2 A x2 n 2.38 A 2.38 200 !0.01176 0.1084 ISSN Encoder In None Using Barcode maker for Software Control to generate, create ISSN  13 image in Software applications. Encoding UPC A In Java Using Barcode printer for Java Control to generate, create UCC  12 image in Java applications. 7.53. Find the maximum value of C for all 2
EAN / UCC  13 Drawer In Java Using Barcode printer for Java Control to generate, create UPC  13 image in Java applications. Draw Code39 In Java Using Barcode maker for Eclipse BIRT Control to generate, create ANSI/AIM Code 39 image in Eclipse BIRT applications. 2 tables that could arise in Problem 7.13.
Barcode Creation In .NET Using Barcode printer for VS .NET Control to generate, create bar code image in .NET framework applications. Bar Code Encoder In None Using Barcode generator for Font Control to generate, create bar code image in Font applications. The maximum value of C occurs when the two classifications are perfectly dependent or associated. In such cases, all those who take the serum will recover and all those who do not take the serum will not recover. The contingency table then appears as in Table 721. Table 721 Recover Group A (using serum) Group B (not using serum) TOTAL 100 0 100 Do Not Recover 0 100 100 TOTAL 100 100 200 Barcode Generator In Visual Basic .NET Using Barcode drawer for .NET framework Control to generate, create bar code image in VS .NET applications. UPC A Printer In Visual Studio .NET Using Barcode creator for ASP.NET Control to generate, create UPCA Supplement 2 image in ASP.NET applications. Since the expected cell frequencies, assuming complete independence, are all equal to 50, x2 (100 50 50)2 (0 50)2 50 (0 50)2 50 (100 50 50)2 200 Then the maximum value of C is 2x2 >(x2 n) 2200>(200 200) 0.7071. In general, for perfect dependence in a contingency table where the numbers of rows and columns are both equal to k, the only nonzero cell frequencies occur in the diagonal from upper left to lower right. For such cases, Cmax 2(k 1)>k. Miscellaneous problems 7.54. An instructor gives a short quiz involving 10 truefalse questions. To test the hypothesis that the student is guessing, the following decision rule is adopted: (i) If 7 or more are correct, the student is not guessing; (ii) if fewer than 7 are correct, the student is guessing. Find the probability of rejecting the hypothesis when it is correct. Let p probability that a question is answered correctly. The probability of getting x questions out of 10 correct is 10Cx pxq10 x, where q Then under the hypothesis p 0.5 (i.e., the student is guessing), 1 p. CHAPTER 7 Tests of Hypotheses and Significance
P(7 or more correct) P(7 correct) 10C7 2 Therefore, the probability of concluding that the student is not guessing when in fact he is guessing is 0.1719. Note that this is the probability of a Type I error. 1 3 2 P(8 correct) 1 10C8 2 1 2 2 P(9 correct) 10C9 2 P(10 correct) 1 2 10C10 2 7.55. In Problem 7.54, find the probability of accepting the hypothesis p
Under the hypothesis p P(less than 7 correct) 1 1 0.7, P(7 or more correct) [10C7(0.7)7(0.3)3 10C8(0.7) 0.5 when actually p
(0.3)2 10C9(0.7) (0.3) 10C10(0.7) 7.56. In Problem 7.54, find the probability of accepting the hypothesis p 0.5 when actually (a) p (b) p 0.8, (c) p 0.9, (d) p 0.4, (e) p 0.3, (f) p 0.2, (g) p 0.1. (a) If p 1 0.6, the required probability is given by [P(7 correct) 1 P(8 correct) P(9 correct) 10C8(0.6) 0.6, P(10 correct)] 10C9(0.6) [10C7(0.6)7(0.4)3 (0.4)2 (0.4) 10C10(0.6) The results for (b), (c), . . . , (g) can be similarly found and are indicated in Table 722 together with the value corresponding to p 0.7 found in Problem 7.55. Note that the probability is denoted by b (probability of a Type II error). We have also included the entry for p 0.5, given by b 1 0.1719 0.828 from Problem 7.54. Table 722 p b 0.1 1.000 0.2 0.999 0.3 0.989 0.4 0.945 0.5 0.828 0.6 0.618 0.7 0.350 0.8 0.121 0.9 0.013 7.57. Use Problem 7.56 to construct the graph of b vs. p, the operating characteristic curve of the decision rule in Problem 7.54. The required graph is shown in Fig. 714. Note the similarity with the OC curve of Problem 7.27.
Fig. 714 If we had plotted (1 b) vs. p, the power curve of the decision rule would have been obtained. The graph indicates that the given decision rule is powerful for rejecting p 0.5 when actually p 7.58. A coin that is tossed 6 times comes up heads 6 times. Can we conclude at (a) 0.05, (b) 0.01 significance level that the coin is not fair Consider both a onetailed and a twotailed test.

