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An official Journal of the Institute of Mathematical Statistics. e. – If read this article p-value is greater than . Hence, if m is the average weekly earnings in managerial and professional positions for men, the hypotheses to be tested are H0 : m= 670versusHa : m 670 ©1998 Brooks/Cole Publishing/ITP The rejection region for this one-tailed test consists of large values of or, equivalently, values of the standardized test statistic z in the right tail of the standard normal distribution, with a= .
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The probability that you have made an incorrect decision is a= . g. • If the p-valuelies between . • You can have a two-tailed test of a hypothesis or a one-tailed test of a hypothesis, a left tailed-test or a right-tailed test. e. 03.
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• Perform the test: Compute the test statistic • Conclusion: We compare the computed value of test statistic in step (iv) with the significant value at the given level of significance, if it fall in critical region reject and if it fall in acceptance region accept null hypothesis. 4 and 9. Do these data indicate that the participation rate for adults over 40 years of age is significantly less than the 20% figure? Calculate the p-valueand use it to draw the appropriate conclusions. A Statistical test of hypotheses 2.
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e. ©1998 Brooks/Cole Publishing/ITPLarge-Sample Statistical Test for (m1-m2): 1. 0012)=. ii) New process is inferior to standard process. Ten individuals are chosen at random from normal population and their heights are found to be 63, 66, 67, 68, 69, 70, 71 inches. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University.
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6 A Large-Sample Test of Hypothesis for the Difference Between Two Binomial Proportions Large-Sample Statistical Test forp1-p2 : 1. ØSimple random sampling ØStratified random sampling ØSystematic sampling Terminology • Parameter: Any population constant is called parameter. The modified test statistic is Although this test statistic is not used often, the procedure is no different from other large-sample tests you have already mastered! ©1998 Brooks/Cole Publishing/ITP9. is an international journal publishing high-quality, original research papers additional hints a wide spectrum of pure and applied mathematics. • Null Hypothesis (H 0): In hypothesis testing, a statistician or decision-maker should be completely impartial and should not allow his personal views to influence the decision.
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Do men in the same positions have average weekly earnings that are higher than those for women? A random sample of n= 40 men in managerial and professional positions showed = $725 and s= $102. The results are statistically significant. • Example 9. 4 A Large-Sample Test of Hypothesis for the Difference Between Two Population Means • In testing whether the difference in sample means indicates that the true difference in populations means differs from a specified value, (m1-m2) = D0, you can use the standard error of the difference in sample means: in the form of a z statistic to measure how many standard deviations the difference lies from the hypothesized difference D0. ©1998 Brooks/Cole Publishing/ITP 4.
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For this rejection region, the value of a is the p-value: p-value =P(z 3. • The unnumbered figures on page 344 show one- and two-tailed rejection regions: ©1998 Brooks/Cole Publishing/ITPCalculating the p-Value To avoid any ambiguity in their conclusions, some experimenters prefer to use a variable level of significance called the p-value for the test. Null hypothesis: H0 : p = p0 2. e.
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e. 33: H 0 is accepted with 1% level of significance Important Remark: • Theoretically: n 100 for large sample • Practically: n 30 for large sample Statistics and normal Z- variate: • Single Mean: • Difference of Means: • Single S. 0024 Notice that the two-tailedp-valueis actually twice the tail area corresponding to the calculated value of the test statistic. .