# chp8 - CHAPTER 8...

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1 CHAPTER 8 Homework:1,3,7,17,23,26,31,33,39,41,47,49,55,61, 67,69,100,107,109ab Sec 8.1: Elements of a hypothesis Testing: (1) Set up hypotheses A hypothesis is simply a statement about a population parameter, e.g. the population mean. There are two types of hypotheses -- the null hypothesis and alternative hypothesis.

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2 A NULL HYPOTHESIS is a hypothesis to be tested. Typically, we believe that null-hypothesis is true unless the data provide enough evident that it is false. AN ALTERNATIVE HYPOTHESIS is a hypothesis that contradicts the null-hypothesis. If the null hypothesis is rejected by a test, then we believe the alternative hypothesis is true.
3 Remember: If the null hypothesis is not rejected by a test, we can not infer that the null hypothesis is true. That is, a hypotheses test can only prove (with a confidence) that the alternative may be true, but never the null. Because of this special feature of a hypotheses testing procedure, the alternative hypothesis is usually set up as a hypothesis that is hoped to be shown to be true by the test.

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4 TWO-TAILED ALTERNATIVE If the alternative states that a population parameter is different from a specific value. The corresponding test is called a two-tailed test. RIGHT-TAILED ALTERNATIVE If the alternative states that a population parameter is greater than a specific value. The corresponding test is called a right-tailed test. LEFT-TAILED ALTERNATIVE If the alternative states that a population parameter is less than a specific value. The corresponding test is called a left-tailed test.
5 (EX 8.1) (Basic-- Set up the hypotheses) The R.R Bowker company of New-York collects information on the retail prices of books. In 1986, the mean retail price of all hardcover history books was \$28.44. Suppose you want to know whether the mean retail price of this kind of books is higher than \$28.44 this year. Can you set up a test answering your problem? (a). Determine the alternative hypothesis. (b). Determine the null hypothesis. (c). What type of hypothesis it is?

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6 (EX 8.2) (Basic -- Set up the hypotheses ) High airline occupancy rates on scheduled flights are essentially to profitability. Suppose that a scheduled flight must average at least 60% occupancy rate to be profitable. We know that the occupancy rate of the Sunday morning flight from Orlando to New-York City is only 54%. Before the company decides to close this scheduled flight, they ask you to set up a test helping them to make their decision. (a). What should be the alternative hypothesis if the company's goal is to close this flight? (b). What is the null hypothesis?
7 (2) Compute the test statistic We already discussed that there are several different types of statistics to measure the central tendency of a population. Also, there are several different test statistics for testing about a population mean. For example, there are z-statistic and t-statistic.

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chp8 - CHAPTER 8...

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