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Unformatted text preview: & & 8.1 In this exercise, the parameter of interest is , the population mean. The objective of the experiment is to show that the mean exceed 2.3. a. We want to prove the alternative hypothesis that is, in fact, greater than 2.3. Hence, the alternative hypothesis is H a : > 2.3 and the null hypothesis is H : = 2.3 b. the probability of a Type I error is defined as & = P[reject H 0 when H is true] = P[decide > 2.3 when = 2.3] c. The best estimator for is the sample average x , and the test statistics is n x z  = which represent the distance (measured in units if standard deviations) from x to the hypothesized mean . In order to perform the test at significance level & =.05, given the hypotheses above, we complete the following steps: (i) The value of the test statistic is 04 . 2 35 / 29 . 3 . 2 4 . 2 * = = z (ii) Pvalue = ( ) ( ) 0207 . 04 . 2 * = > = > Z P z Z P , which we find with the help of the Normal Table (iii) The pvalue of 0.0207 is smaller than the significance level ( & =.05). Therefore, we reject the null hypothesis (iv) The conclusion is that there is evidence in the sample that the population mean is larger than 2.3. 8.2. If the experimenter wishes to prove that < 2.9, this is the alternative hypothesis. Hence, the hypothesis to be tested is H : = 2.9 H a : < 2.9 and the test is onetailed. Lets perform the test at significance level & =.05. (i) The value of the test statistic (the same zstatistic from 8.1), is 2 . 10 35 / 29 . 9 . 2 4 . 2 * = = z (ii) Pvalue = ( ) 2 . 10  < Z P (iii) The pvalue of 0 is smaller than the significance level level ( & =.05). Therefore, we reject the null hypothesis (iv) The conclusion is that there is evidence in the sample that the population mean is smaller than 2.9. 8.3. If the experimenter wishes to prove that & 2.9, this is the alternative hypothesis. Hence, the hypothesis to be tested is H : = 2.9 H a : & 2.9 and the test is twotailed....
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This note was uploaded on 10/02/2009 for the course PSTAT 5E taught by Professor Eduardomontoya during the Spring '08 term at UCSB.
 Spring '08
 EduardoMontoya

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