One thousand respondents were asked to watch an eight

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One thousand respondents were asked to watch an eight-minute segment of the DIY Network show House Crashers on their computer (to simulate television watching). Four 30-second television ads were embedded following the first four minutes of the show (two for lawn or garden equipment and two for paint), followed by four additional minutes of the show. The study was blind in that respondents did not know its purpose. Ad order was randomized for each respondent to eliminate order bias. In a subsequent online survey, respondents provided both aided and unaided recall measurements of the television spots (to assess which elements in the ads were most memorable), as well as information on how the ads affected perceptions of each brand featured and brand awareness. Several red-herring questions were
introduced to ensure participants would not be swayed by their perceived purpose of the study or the merchandise category. The test did showcase unique differences in the way consumers process television advertising based on whether they are in-market or not-in-market for lawn and garden products. The survey Marcus Thomas used is available in Connect. Exhibit 14-4 compares the statistical situation to the legal one. One of two conditions exists in nature—either the null hypothesis is true or the alternative hypothesis is true. An indicted person is innocent or guilty. Two decisions can be made about these conditions: one may accept the null hypothesis or reject it (thereby accepting the alternative hypothesis). Two of these situations result in correct decisions; the other two lead to decision errors . > Exhibit 14-4 Comparison of Statistical Decisions to Legal Analogy When a Type I error (α) is committed, a true null hypothesis is rejected; the innocent person is unjustly convicted. The value is called the level of
significance and is the probability of rejecting the true null hypothesis. With a Type II error (β) , one fails to reject a false null hypothesis; the result is an unjust acquittal, with the guilty person going free. In our system of justice, it is more important to reduce the probability of convicting the innocent than that of acquitting the guilty. Similarly, hypothesis testing places a greater emphasis on reducing Type I errors than on Type II errors . Type I Error Assume the hybrid manufacturer’s problem is complicated by a consumer testing agency’s assertion that the average city miles per gallon (mpg) has changed. Assume the population mean is 50 mpg, the standard deviation of the population is 10 mpg, and the size of the sample is 25 vehicles. With this information, we can calculate the standard error of the mean (σ X ) (the standard deviation of the distribution of sample means). This hypothetical distribution is pictured in Exhibit 14-5 . The standard error of the mean is calculated to be 2 mpg:
Exhibit 14-5 Probability of Making a Type I Error Given H 0 Is True If the decision is to reject H 0 with a 95 percent confidence interval (α = . 05), a Type I error of .025 in each tail is accepted (this assumes a two-tailed test). In part A of Exhibit 14-5 , see the regions of rejection indicated by

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