{"id":5353,"date":"2022-08-19T20:13:31","date_gmt":"2022-08-19T20:13:31","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5353"},"modified":"2022-08-19T20:13:59","modified_gmt":"2022-08-19T20:13:59","slug":"11c-in-class-activity","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/11c-in-class-activity\/","title":{"raw":"11C In-Class Activity","rendered":"11C In-Class Activity"},"content":{"raw":"The Federal Trade Commission (FTC) is a bipartisan federal agency in the United\u00a0 States. It was created in 1914 under President Woodrow Wilson. Its goal is to enforce\u00a0 \u201cfederal consumer protection laws that prevent fraud, deception, and unfair business\u00a0 practices.\u201d[footnote]Federal Trade Commission. (n.d.). Enforcement<\/em>. https:\/\/www.ftc.gov\/enforcement [\/footnote]\r\n\r\n\"\"\r\n\r\nCredit: iStock\/lldo Frazao\r\n
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Question 1<\/h3>\r\nDo you think it is important to have these protections in place?\r\n\r\n<\/div>\r\n
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Question 2<\/h3>\r\nIn the preview assignment, you were told that in 2020, the national percentage of\u00a0 complaints to the FTC due to identity theft was 29.4%. A commission in Florida is\u00a0 asked to study the complaints locally and to determine whether Florida is exceeding\u00a0 the national trend. Complete the following table to understand which observed\u00a0 sample proportions might be unusual.\r\n
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Number of\u00a0 complaints\u00a0 due to\r\n\r\nidentity\r\n\r\ntheft (out of\u00a0 500)<\/td>\r\nValue of [latex] \\hat{p} [\/latex], the sample\r\n\r\nproportion<\/td>\r\n[latex] z = \\frac{\\hat{p}-0.294}{0.0204} [\/latex]<\/td>\r\nP-value<\/td>\r\nDo you think\u00a0 we have\r\n\r\nconvincing\r\n\r\nevidence to\r\n\r\nsuggest that\u00a0 Florida is\r\n\r\nexceeding the\u00a0 national\r\n\r\ntrend? Why?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
148<\/td>\r\n0.296<\/td>\r\n[latex] z [\/latex]\u00a0= 0.098<\/td>\r\n0.461<\/td>\r\nNo, because a\u00a0 sample\r\n\r\nproportion of\u00a0 0.296 is not\r\n\r\nthat unlikely\r\n\r\ngiven the\r\n\r\nnational trend\u00a0 of 0.294.<\/td>\r\n<\/tr>\r\n
150<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
155<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
160<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
165<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
170<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
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Question 3<\/h3>\r\nAt what point does it appear that something unusual or unexpected is happening in\u00a0 Florida? That is, how many identity theft claims out of 500 total claims would make\u00a0 you think that Florida is exceeding the national trend?\r\n\r\n<\/div>\r\nSuppose that in a sample of 500 claims, 460 of them were because of identity theft. If\u00a0 the true population proportion is really 0.294<\/em>, is it reasonable to observe a random\u00a0 sample proportion of\u00a0[latex] \\hat{p} = \\frac{460}{500} = 0.92[\/latex]? Was this particular group of 500 people just\u00a0\u00a0incredibly unusual OR could it be that the population proportion is something else,\u00a0 which allows us to reject the null hypothesis?\r\n\r\nA P-value assists us in determining whether or not we have evidence to reject the null\u00a0 hypothesis. In statistics, we establish a \u201ccut-off\u201d value. There is no absolute cut-off\u00a0 value, but typically we use 5%.\r\n\r\nThis 5% represents the extreme areas under the curve, which means they represent\u00a0 unusual values. We compare the P-value to [latex] \\alpha [\/latex], which is the significance level of the\u00a0 test. The significance level, [latex] \\alpha [\/latex], is the cut-off for P-values at which we have enough\u00a0 evidence to reject the null hypothesis. Typically, small significance levels such as 1%,\u00a0 5%, or 10% are used in hypothesis testing. You will learn more about significance levels\u00a0 and their importance in In-Class Activity 11.E.\r\n\r\nIn order to make a claim about the null hypothesis, we write\u00a0[latex] \\alpha[\/latex] as a decimal and\u00a0 compare it to the P-value, as follows:\r\n