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barcode font reporting services Tests of Hypotheses and Significance in Software
CHAPTER 7 Tests of Hypotheses and Significance Decode QR Code In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Quick Response Code Maker In None Using Barcode creation for Software Control to generate, create QR Code image in Software applications. Fig. 77 Decoding QR Code JIS X 0510 In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Creating QRCode In C#.NET Using Barcode generation for VS .NET Control to generate, create Quick Response Code image in .NET framework applications. 7.26. A company manufactures rope whose breaking strengths have a mean of 300 lb and standard deviation 24 lb. It is believed that by a newly developed process the mean breaking strength can be increased, (a) Design a decision rule for rejecting the old process at a 0.01 level of significance if it is agreed to test 64 ropes, (b) Under the decision rule adopted in (a), what is the probability of accepting the old process when in fact the new process has increased the mean breaking strength to 310 lb Assume that the standard deviation is still 24 lb. QR Code ISO/IEC18004 Creator In Visual Studio .NET Using Barcode generation for ASP.NET Control to generate, create QRCode image in ASP.NET applications. QR Code Creator In .NET Using Barcode drawer for VS .NET Control to generate, create QR Code image in VS .NET applications. (a) If m is the mean breaking strength, we wish to decide between the hypotheses H0: m H1: m 300 lb, and the new process is equivalent to the old one 300 lb, and the new process is better than the old one QR Code JIS X 0510 Encoder In Visual Basic .NET Using Barcode creation for VS .NET Control to generate, create Quick Response Code image in VS .NET applications. Bar Code Encoder In None Using Barcode creator for Software Control to generate, create barcode image in Software applications. For a onetailed test at a 0.01 level of significance, we have the following decision rule (refer to Fig. 78): (1) Reject H0 if the z score of the sample mean breaking strength is greater than 2.33. (2) Accept H0 otherwise. # m X # 300 # X Since Z , X 300 s> !n 24> !64 Therefore, the above decision rule becomes: # 2.33, X Bar Code Creation In None Using Barcode encoder for Software Control to generate, create bar code image in Software applications. Create European Article Number 13 In None Using Barcode drawer for Software Control to generate, create European Article Number 13 image in Software applications. 3z. Then if Z
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GS1 128 Decoder In C# Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications. Data Matrix Decoder In VB.NET Using Barcode scanner for .NET framework Control to read, scan read, scan image in .NET applications. Fig. 78 Encoding UPC Code In C#.NET Using Barcode printer for .NET framework Control to generate, create UPCA Supplement 2 image in .NET framework applications. EAN13 Creation In None Using Barcode encoder for Font Control to generate, create EAN13 Supplement 5 image in Font applications. Fig. 79 (b) Consider the two hypotheses (H0: m 300 lb) and (H1: m 310 lb). The distributions of breaking strengths corresponding to these two hypotheses are represented respectively by the left and right normal distributions of Fig. 79. The probability of accepting the old process when the new mean breaking strength is actually 310 lb is represented by the region of area b in Fig. 79. To find this, note that 307.0 lb in standard units is (307.0 310) > 3 1.00; hence b area under righthand normal curve to left of z 1.00 0.1587 CHAPTER 7 Tests of Hypotheses and Significance
This is the probability of accepting (H0: m probability of making a Type II error. 300 lb) when actually (H1: m 310 1b) is true, i.e., it is the
7.27. Construct (a) an OC curve, (b) a power curve for Problem 7.26, assuming that the standard deviation of breaking strengths remains at 24 lb. By reasoning similar to that used in Problem 7.26(b), we can find b for the cases where the new process yields mean breaking strengths m equal to 305 lb, 315 lb, etc. For example, if m 305 lb, then 307.0 lb in standard units is (307.0 305)>3 0.67, and hence b area under right hand normal curve to left of z 0.67 0.7486 In this manner Table 74 is obtained. Table 74 m b 290 1.0000 295 1.0000 300 0.9900 305 0.7486 310 0.1587 315 0.0038 320 0.0000 (a) The OC curve is shown in Fig. 710(a). From this curve we see that the probability of keeping the old process if the new breaking strength is less than 300 lb is practically 1 (except for the level of significance of 0.01 when the new process gives a mean of 300 lb). It then drops rather sharply to zero so that there is practically no chance of keeping the old process when the mean breaking strength is greater than 315 lb. (b) The power curve shown in Fig. 710(b) is capable of exactly the same interpretation as that for the OC curve. In fact the two curves are essentially equivalent. Fig. 710 7.28. To test the hypothesis that a coin is fair (i.e., p 0.5) by a number of tosses of the coin, we wish to impose the following restrictions: (A) the probability of rejecting the hypothesis when it is actually correct must be 0.05 at most; (B) the probability of accepting the hypothesis when actually p differs from 0.5 by 0.1 or more (i.e., p 0.6 or p 0.4) must be 0.05 at most. Determine the minimum sample size that is necessary and state the resulting decision rule. Here we have placed limits on the risks of Type I and Type II errors. For example, the imposed restriction (A) requires that the probability of a Type I error is a 0.05 at most, while restriction (B) requires that the probability of a Type II error is b 0.05 at most. The situation is illustrated graphically in Fig. 711. Fig. 711

