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9-91. Suppose that we wish to test H0: 0 versus H1: 0 , where the population is normal with known . Let 0 , and de ne the critical region so that we will reject H0 if z0 z or if z0 z , where z0 is the value of the usual test statistic for these hypotheses. (a) Show that the probability of type I error for this test is . (b) Suppose that the true mean is 1 . Derive 0 an expression for for the above test. 9-92. Derive an expression for for the test on the variance of a normal distribution. Assume that the twosided alternative is speci ed. 9-93. When X1, X2, p , Xn are independent Poisson random variables, each with parameter , and n is large, the sample mean X has an approximate normal distribution with mean and variance n. Therefore, Z X 1 n 9-94. When X1, X2, p , Xn is a random sample from a normal distribution and n is large, the sample standard deviation has approximately a normal distribution with mean and variance 2 12n2 . Therefore, a large-sample test for H0: 0 can be based on the statistic 2 S

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2 0 0

12n2

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The System.dll file contains the Trace class, which can be used to obtain information while the system is running. At times, such as when working with a multitier or multithreaded application, using the debugger to retrieve data doesn t work. This is where tracing can provide troubleshooting data. You enable tracing by adding the /d:TRACE=True switch when compiling the code. By default, the trace switch is enabled in Visual Studio .NET, which means that trace code is compiled into the debug and release builds of applications, which produces instrumented builds. Instrumentation provides the ability to monitor the health of an application running in real time. Tracing helps isolate problems without disturbing a running application. All the methods of the Debug class are included in the trace. Two Trace classes exist: System.Diagnostics.Trace and System.Web.UI.Page .Trace. The System.Diagnostics.Trace class is covered here, and System.Web .UI.Trace is covered later in this chapter. To ensure that the correct Trace class is used, you can specify the full path to System.Diagnostics.Trace, or create an alias at the top of the Web page as follows:

has approximately a standard normal distribution. Thus we can test H0: in Z by 0. When Xi 0 by replacing are Poisson variables, this test is preferable to the largesample test of Section 9-2.5, which would use S 1n in the denominator, because it is designed just for the Poisson distribution. Suppose that the number of open circuits on a semiconductor wafer has a Poisson distribution. Test data for 500 wafers indicate a total of 1038 opens. Using 0.05, does this suggest that the mean number of open circuits per wafer exceeds 2.0

Use this result to test H0: 10 versus H1: 10 for the golf ball overall distance data in Exercise 6-25. 9-95. Continuation of Exercise 9-94. Using the results of the previous exercise, nd an approximately unbiased estimator of the 95 percentile 1.645 . From the fact that X and S are independent random variables, nd the standard error of . How would you estimate the standard error 9-96. Continuation of Exercises 9-94 and 9-95. Consider the golf ball overall distance data in Exercise 6-25. We wish to investigate a claim that the 95 percentile of overall distance does not exceed 285 yards. Construct a test statistic that can be used for testing the appropriate hypotheses. Apply this procedure to the data from Exercise 6-25. What are your conclusions 9-97. Let X1, X2, p , Xn be a sample from an exponential distribution with parameter . It can be shown that n 2 i 1 Xi has a chi-square distribution with 2n degrees of freedom. Use this fact to devise a test statistic and critical region for H0: 0 versus the three usual alternatives.

Click in the ruler where you want to insert the tab. Click at the end of the text after which you want to add a tab. Press .

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