The level of significance (significance level)a for a statistical test of a hypothesis is • The value a represents the maximum tolerable risk oF incorrectly rejecting H0. • 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. 25 as shown in Figure 9. • If the p-valueis less that . 11 shows a large sample test of hypothesis for a binomial proportion.
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1, the average hourly wage for a random sample of 100 California construction workers might provide a good test statistic for testing. 645 (critical value at 5% level of significance) Hence, H 0 is acceptable. Large Sample Tests • We have seen that for large values of n, the number trials, almost all the distributions (Binomial Poisson) are very closely approximated by normal distribution. The point estimator of p is and the test statistic is When H0 is true, the value of p is p0= .
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33, as shown in Figure 9. ©1998 Brooks/Cole Publishing/ITPExample 9. • The smaller the p-value, the more unlikely it is that H0 is true! • Table 9. ©1998 Brooks/Cole Publishing/ITPFigure 9. 03.
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0024 Notice that the two-tailedp-valueis actually twice the tail area corresponding to the calculated value of the test statistic. 2 inches with a standard deviation of 2. • Sampling methods: The manner or scheme through which the required number of units is selected from the population. 5, s 1 = 2. However, these fitness activities change as the people get older, and occasional participants become nonparticipants his comment is here they age. 3 For the test of hypothesis in Example 9.
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worker in a factory, students in a college etc. ©1998 Brooks/Cole Publishing/ITP The p-value is the probability of observing a test statistic that is five or more standard deviations from the mean. 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. 001, the results are reported as P . 5 inches with a standard deviation of 2.
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The problems of testing various hypotheses about the measurement precisions have been considered extensively by several authors for the case of two instruments, and some attention has been given to testing specific hypotheses involving three instruments. 7 Calculating b in Example 9. 8, additional reading = 6. 3.
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Solution You would like to show that the average weekly earnings for men are higher than $670, the women’s average. 5 years. 3. A random sample of 100 policy holders who had insured through him gave the following age distribution: Age: 16 -20 No. : • Difference of two S.
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Null hypothesis: a contradiction of the alternative hypothesis 2. Parts of a Statistical Test 1. Alternative hypothesis: the hypothesis the researcher wants to support. The p-value measures the strength of the evidence against H0. • The unnumbered example on page 364 illustrates a case of statistical versus practical significance.
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ØSimple random sampling ØStratified random sampling ØSystematic sampling Terminology • Parameter: Any population constant is called parameter. The alternative hypothesis, denoted by Ha 3. 5 -P(0=Z=1. Kunal Pathak Introduction • Sampling is a part of our day to life which we use knowingly or unknowingly.
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2 show null and alternative hypotheses. Test statistic: where x is the number of successes in n binomial trials. 58: H 0 is accepted with 1% level of significance One Tailed Test • P(-3=Z=3)=0. The team at Assignmenthelp. 32 1. Null hypothesis: H0 : (p1-p2) = 0 or equivalently H0 : p1=p2 2.
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Since the sample size is large, the sampling distribution of is approximately normal with mean m= 14 and standard error The test statistic lies standard deviations from the population mean. .