# The other group used an assembly line that moved at a

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the other group used an assembly line that moved at a fixed pace. After two weeks, all the workers took a test of job satisfaction. Then they switched work set-ups and took the test again after two more weeks. The response variable is the difference in satisfaction scores, self-paced minus machine-paced. State appropriate hypotheses for performing a significance test. The parameter of interest is the mean µ of the differences ( self-paced minus machine-paced ) in job satisfaction scores in the population of all assembly- line workers at this company. Because the initial question asked whether job satisfaction differs, the alternative hypothesis is two-sided; that is, either µ < 0 or µ > 0. For simplicity, we write this as µ 0. That is: H 0 : µ = 0 H a : µ 0 24 Test Statistic A test of significance is based on a statistic that estimates the parameter that appears in the hypotheses. When H 0 is true, we expect the estimate to take a value near the parameter value specified in H 0 . Values of the estimate far from the parameter value specified by H 0 give evidence against H 0 . A test statistic calculated from the sample data measures how far the data diverge from what we would expect if the null hypothesis H 0 were true. Large values of the statistic show that the data are not consistent with H 0 . z estimate - hypothesized value standard deviation of the estimate
11/17/2012 5 25 P- Value The null hypothesis H 0 states the claim that we are seeking evidence against . The probability that measures the strength of the evidence against a null hypothesis is called a P -value . The probability, computed assuming H 0 is true, that the statistic would take a value as extreme as or more extreme than the one actually observed is called the P -value of the test. The smaller the P -value, the stronger the evidence against H 0 provided by the data. Small P -values are evidence against H 0 because they say that the observed result is unlikely to occur when H 0 is true. Large P -values fail to give convincing evidence against H 0 because they say that the observed result is likely to occur by chance when H 0 is true. 26 Statistical Significance The final step in performing a significance test is to draw a conclusion about the competing claims you were testing. We will make one of two decisions based on the strength of the evidence against the null hypothesis (and in favor of the alternative hypothesis) ʊ reject H 0 or fail to reject H 0 . If our sample result is too unlikely to have happened by chance assuming H 0 is true, then we ll reject H 0 . Otherwise, we will fail to reject H 0 . Note: A fail-to-reject H 0 decision in a significance test doesn’t mean that H 0 is true. For that reason, you should never accept H 0 or use language implying that you believe H 0 is true. In a nutshell, our conclusion in a significance test comes down to: P -value small ĺ reject H 0 ĺ conclude H a (in context) P -value large ĺ fail to reject H 0 ĺ cannot conclude H a (in context)
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