lecture_6_2 - Introduction to inference Tests of...

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    Introduction to inference   Tests of significance IPS chapter 6.2 © 2006 W.H. Freeman and Company
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Objectives (IPS chapter 6.2) Tests of significance Null and alternative hypotheses One-sided and two-sided tests The P -value Tests for a population mean The significance level α Confidence intervals to test hypotheses
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We have seen that the properties of the sampling distribution of x bar help us estimate a range of likely values for population mean μ . We can also rely on the properties of the sample distribution to test hypotheses. Example: You are in charge of quality control in your food company. You sample randomly four packs of cherry tomatoes, each labeled 1/2 lb. (227 g). The average weight from your four boxes is 222 g. Obviously, we cannot expect boxes filled with whole tomatoes to all weigh exactly half a pound. Thus, Is the somewhat smaller weight simply due to chance variation? Is it evidence that the calibrating machine that sorts cherry tomatoes into packs needs revision?
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Null and alternative hypotheses A test of statistical significance tests a specific hypothesis using sample data to decide on the validity of the hypothesis. In statistics, a hypothesis is an assumption or a theory about the characteristics of one or more variables in one or more populations. What you want to know: Does the calibrating machine that sorts cherry tomatoes into packs need revision? The same question reframed statistically: Is the population mean µ for the distribution of weights of cherry tomato packages equal to 227 g (i.e., half a pound)?
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The null hypothesis is a very specific statement about a parameter of the population(s). It is labeled H 0 . The alternative hypothesis is a more general statement about a parameter of the population(s) that is exclusive of the null hypothesis. It is labeled H a .
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