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Unformatted text preview: 7.2 THE LANGUAGE OF STATISTICAL DECISION MAKING DEFINITIONS: The population is the entire group of objects or individuals under study, about which information is desired. A sample is a part of the population that is actually used to get information. Statistical inference is the process of drawing conclusions about the population based on information from a sample of that population. DEFINITIONS: The null hypothesis , denoted by H , is the conventional belief--the status quo, or prevailing viewpoint, about a population. The alternative hypothesis , denoted by H 1 , is an alternative to the null hypothesis the statement that there is an effect, a difference, a change in the population. Tip: Having trouble determining the alternative hypothesis? Ask yourself Why is the research being conducted? The answer is generally the alternative hypothesis, which is why the alternative hypothesis is often referred to as the research hypothesis. Aspirin Cuts Cancer Risk Problem 1 According to the American Cancer Society, the lifetime risk of developing colon cancer is 1 in 16. A study suggests that taking an aspirin every other day for 20 years can cut your risk of colon cancer nearly in half. However, the benefits may not kick in until at least a decade of use. (a) Write the null and the alternative hypotheses for this setting. (b) Is this a one-sided to the right, one- sided to the left, or two-sided alternative hypothesis? Hint : look at the alternative hypothesis. Solution 1 (a) H : Taking an aspirin every other day for 20 years will not change the risk of getting colon cancer, which is 1 in 16. H 1 : Taking an aspirin every other day for 20 years will reduce the risk of getting colon cancer, so the risk will be less than 1 in 16. (b) The alternative hypothesis is one-sided to the left. Average Life Span Problem 2 Suppose you work for a company that produces cooking pots with an average life span of seven years. To gain a competitive advantage, you suggest using a new material that claims to extend the life span of the pots. You want to test the hypothesis that the average life span of the cooking pots made with this new material increases. (a) Write the null and the alternative hypotheses for this setting....
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- Summer '11