Introduction to Probability and Statistics for Engineers and Scientists
304 Chapter 8:Hypothesis Testing and so thep-value is given by p-value=P{Z<−.336}, Z∼N(0, 1) =.368 Since this value is greate ...
8.3Tests Concerning the Mean of a Normal Population 305 TABLE 8.1 X 1 ,...,XnIs a Sample from aN(μ,σ^2 )Populationσ^2 Is KnownX= ...
306 Chapter 8:Hypothesis Testing Now whenσ^2 is no longer known, it seems reasonable to estimate it by S^2 = ∑n i= 1 (Xi−X)^2 n− ...
8.3Tests Concerning the Mean of a Normal Population 307 Accept −t 0 ta n(X − m^0 )/S 2 , n − 1 a 2 , n − 1 FIGURE 8.3 The two-si ...
308 Chapter 8:Hypothesis Testing groups — one group to receive the drug and the other to receive a placebo (that is, a tablet th ...
8.3Tests Concerning the Mean of a Normal Population 309 against the one-sided alternative H 1 :μ>μ 0 The significance levelαt ...
310 Chapter 8:Hypothesis Testing A computation gives that X=37.2833, S=2.7319 and so the value of the test statistic is T= √ 12( ...
8.3Tests Concerning the Mean of a Normal Population 311 EXAMPLE 8.3j In a single-server queueing system in which customers arriv ...
312 Chapter 8:Hypothesis Testing 8.4Testing the Equality of Means of Two Normal Populations A common situation faced by a practi ...
Populations 8.6.1 Testing the Equality of Parameters in Two Bernoulli has a standard normal distribution; and thus PH 0 ...
314 Chapter 8:Hypothesis Testing SOLUTION A simple computation (or the use of Program 8.4.1) shows that the value of the test st ...
8.4Testing the Equality of Means of Two Normal Populations 315 0 Area = a −ta,k Area = a ta,k FIGURE 8.5 Density of a t-random v ...
316 Chapter 8:Hypothesis Testing If the value of the test statisticTisv, then thep-value is given by p-value=P{Tn+m− 2 ≥v} Progr ...
8.4Testing the Equality of Means of Two Normal Populations 317 The value of the t-statistic is −1.898695 The p-value is 0.03607 ...
318 Chapter 8:Hypothesis Testing and the value of the test statistic is TS= −.675 √ .689(1/10+1/12) =−1.90 Sincet0.5,20=1.725, t ...
8.4Testing the Equality of Means of Two Normal Populations 319 The problem of determining an exact levelαtest of the hypothesis ...
320 Chapter 8:Hypothesis Testing this can be tested by accepting H 0 if −tα/2,n− 1 < √ n W Sw <tα/2,n− 1 rejecting H 0 oth ...
8.5Hypothesis Tests Concerning the Variance of a Normal Population 321 8.5Hypothesis Tests Concerning the Variance of a Normal P ...
322 Chapter 8:Hypothesis Testing SOLUTION We will test the hypothesis that the machine is effective, since a rejection of this h ...
8.6Hypothesis Tests in Bernoulli Populations 323 Thus, a significance levelαtest ofH 0 againstH 1 is to accept H 0 if F 1 −α/2,n ...
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