Introduction to Probability and Statistics for Engineers and Scientists
284 Chapter 7: Parameter Estimation 32.LetX 1 ,...,Xn,Xn+ 1 denote a sample from a normal population whose mean μand varianceσ^2 ...
Problems 285 6.68 6.66 6.62 6.72 6.76 6.67 6.70 6.72 6.78 6.66 6.76 6.72 6.76 6.70 6.76 6.76 6.74 6.74 6.81 6.66 6.64 6.79 6.72 ...
286 Chapter 7: Parameter Estimation whereas a sample of 10 specimens of the second yielded the data Type 2: 3,094, 3,106, 3,004, ...
Problems 287 having varianceσi^2 ,i=1, 2, compute a 95 percent two-sided confidence interval forσ 12 /σ 22 when the data are as ...
288 Chapter 7: Parameter Estimation 49.To estimatep, the proportion of all newborn babies that are male, the gender of 10,000 ne ...
Problems 289 58.Determine 100(1−α) percent one-sided upper and lower confidence intervals for θin Problem 57. 59.LetX 1 ,X 2 ,.. ...
290 Chapter 7: Parameter Estimation If the average life of the first 20 chips tested is 4.6 hours, compute the Bayes estimate of ...
Chapter 8 Hypothesis Testing 8.1Introduction As in the previous chapter, let us suppose that a random sample from a population d ...
292 Chapter 8:Hypothesis Testing 8.2Significance Levels Consider a population having distributionFθ, whereθis unknown, and suppo ...
8.3Tests Concerning the Mean of a Normal Population 293 Now, as was previously mentioned, the objective of a statistical test of ...
294 Chapter 8:Hypothesis Testing SinceX= ∑n i= 1 Xi/nis a natural point estimator ofμ, it seems reasonable to accept H 0 ifXis n ...
8.3Tests Concerning the Mean of a Normal Population 295 Accept −za/2 0 za/2 (X^ −^ m^0 ) n s FIGURE 8.1 This can be pictorially ...
296 Chapter 8:Hypothesis Testing The test given by Equation 8.3.3 can be described as follows: For any observed value of the tes ...
8.3Tests Concerning the Mean of a Normal Population 297 will depend on the value ofμ, and so let us defineβ(μ)by β(μ)=Pμ{accepta ...
298 Chapter 8:Hypothesis Testing 1.0 0.8 0.6 0.4 0.2 0 Probability of accepting H^0 n 12345 d = |σm − m^0 | .95 FIGURE 8.2 The O ...
8.3Tests Concerning the Mean of a Normal Population 299 it follows, since is an increasing function, that ( μ 0 −μ 1 σ/ √ n −zα/ ...
300 Chapter 8:Hypothesis Testing ≈ 1 − (.723) ≈.235 Therefore, if the message is sent 20 times, then there is a 76.5 percent cha ...
8.3Tests Concerning the Mean of a Normal Population 301 Hence, the test of the hypothesis 8.3.8 is to rejectH 0 ifX−μ 0 >zασ/ ...
302 Chapter 8:Hypothesis Testing can be obtained as follows: β(μ)=Pμ { X≤μ 0 +zα σ √ n } =P { X−μ σ/ √ n ≤ μ 0 −μ σ/ √ n +zα } = ...
8.3Tests Concerning the Mean of a Normal Population 303 REMARK We can also test the one-sided hypothesis H 0 :μ=μ 0 (orμ≥μ 0 ) v ...
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