Applied Statistics and Probability for Engineers

9-2 TESTS ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN In this section, we consider hypothesis testing about the mean o ...

If the null hypothesis H 0 :  0 is true, , and it follows that the distribution of Z 0 is the standard normal distribution [d ...

We may solve this problem by following the eight-step procedure outlined in Section 9-1.4. This results in The parameter of int ...

9-2.2 P-Values in Hypothesis Tests One way to report the results of a hypothesis test is to state that the null hypothesis was o ...

P-value approach is used, step 6 of the hypothesis-testing procedure can be modified. Specifically, it is not necessary to state ...

where denotes the probability to the left of zin the standard normal distribution. Note that Equation 9-17 was obtained by evalu ...

This approximation is good when is small compared to . For either of the one-sided alternative hypotheses the sample size requi ...

so one set of operating characteristic curves can be used for all problems regardless of the values of  0 and. From examining t ...

Using the Computer Many statistics software packages will calculate sample sizes and type II error probabilities. To illustrate, ...

will be unknown. Furthermore, we may not be certain that the population is well modeled by a normal distribution. In these situa ...

The P-value column in this display indicates that for large sample sizes the observed sample value of would strongly suggest tha ...

300 CHAPTER 9 TESTS OF HYPOTHESES FOR A SINGLE SAMPLE (c) What is the -error if the true mean is   150? (d) What value of nwo ...

normal.The important result upon which the test procedure relies is that if X 1 , X 2 , p,Xnis a random sample from a normal dis ...

EXAMPLE 9-6 The increased availability of light materials with high strength has revolutionized the design and manufacture of go ...

Computations: Since , s 0.02456,  0  0.82, and n 15, we have Conclusions: Since , we reject H 0 and conclude at the 0.05 le ...

304 CHAPTER 9 TESTS OF HYPOTHESES FOR A SINGLE SAMPLE Finally, most computer programs report P-values along with the computed va ...

approximately. Thus, the probability of rejecting H 0 :  0.82 if the true mean exceeds this by 0.02 is approximately 1  1 0. ...

306 CHAPTER 9 TESTS OF HYPOTHESES FOR A SINGLE SAMPLE (a) Test the hypotheses H 0 :  22.5 versus H 1 : 22.5, using  0.05. ...

9-4 HYPOTHESIS TESTS ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION 307 9-4 HYPOTHESIS TESTS ON THE VARIANCE AND ...

308 CHAPTER 9 TESTS OF HYPOTHESES FOR A SINGLE SAMPLE distribution for this test procedure. Therefore, we calculate , the value ...