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pp.164-178 summer 2009

# pp.164-178 summer 2009 - 164 Hypothesis Testing In...

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Hypothesis Testing In statistics, a hypothesis is a statement (a claim) about a population parameter. The statement is later tested by collecting data. The data either supports or refutes the statement (claim) made about the parameter. The process of collecting data and determining whether the data supports or refutes the stated hypothesis is called hypothesis testing. We will restrict our attention to hypothesis testing for a population mean (µ) using a z (in the case where σ is known ) or hypothesis testing for a population mean using a t (in the case where σ is unknown and we are using the sample standard deviation s as an estimate for σ). Examples of hypotheses for a population mean, µ : 1.The mean highway gas mileage for 2010 Honda CRVs is at least 27 mpg ( μ 27). 2.The mean cost for tuition at four-year private universities in the U.S. is no more than \$30,000 ( μ \$30,000 ). 3.The mean thickness of the flange on a 22 inch I- beams is .500 inch (µ = 0.500). 164

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Example 1 : A consumer advocacy group would like to test Honda’s claim that the mean gas mileage is at least 27 mpg (µ ≥ 27), against the opposite claim— that the mean gas mileage is less than 27 (µ < 27). The consumer advocacy group decides to take a random sample of 36 2010 Honda CRVs and determine their highway mpg. It finds that the mean highway mileage for the 36 cars was 26.7 mpg ( x =26.7). Assume that the standard deviation, σ, is known to be 1.8 mpg. How likely were they to get a sample mean of 26.7 mpg or less) if in fact the true highway mileage is 27 mpg or higher? If the probability is sufficiently small we’ll conclude that μ < 27 mpg. Example 2 : To test the claim made by the IOPU (independent organization of private universities) that the mean cost of tuition at private universities in the U.S. is no more than \$30,000 (µ ≤ \$30,000 ) against the opposite claim that the mean is greater than \$30,000 (µ > \$30,000) fifty private universities were randomly sampled and their annual tuition cost recorded. The mean cost for the sample was \$31,550 ( x = \$31,550) with a standard deviation of \$5,400 (s = \$5,400). What is the probability of getting a sample mean this high or higher if the claim that the tuition is no more than \$30,000 per year (µ ≤ \$30,000 ) is true?
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pp.164-178 summer 2009 - 164 Hypothesis Testing In...

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