{"id":5356,"date":"2022-08-19T22:21:50","date_gmt":"2022-08-19T22:21:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5356"},"modified":"2022-08-19T22:26:45","modified_gmt":"2022-08-19T22:26:45","slug":"11c-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/11c-preview\/","title":{"raw":"11C Preview","rendered":"11C Preview"},"content":{"raw":"Preparing for the next class\r\n\r\nIn the next in-class activity, you will need to be able to describe what a P-value measures and identify how a P-value is represented in a statistical distribution.\r\n\r\nYou recently learned that a test statistic is used in hypothesis testing to help measure evidence against a null hypothesis. A test statistic allows us to take standard error into account when considering the evidence provided by a sample statistic. However, recall that the test statistic comes from one observed sample of data. Based on your knowledge of sampling distributions, you know that there are lots of different samples that could have been obtained. Each sample would have its own test statistic.\r\n\r\nIn In-Class Activity 11.A, we learned that the evidence used in hypothesis testing is probability. The statistical evidence that we gather is always evidence in support of the alternative hypothesis and against the null hypothesis. We ask ourselves the question, \u201cDo we have enough evidence to reject the null hypothesis?\u201d\r\n
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Question 1<\/h3>\r\nAccording to a 2021 report published by the Federal Trade Commission (FTC),\u00a0 29.4% of claims to the FTC in 2020 were due to identity theft cases.[footnote]Federal Trade Commission. (2021, February). Consumer sentinel network<\/em>, data book 2020. https:\/\/www.ftc.gov\/system\/files\/documents\/reports\/consumer-sentinel-network-data-book-2020\/csn_annual_data_book_2020.pdf[\/footnote] Suppose that\u00a0 in the state of Florida, a random sample of 500 claims to the FTC are observed.\r\n
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  1. Based on the published national percentage of 29.4%, about how many of\u00a0 the 500 Florida claims would you expect to be due to identity theft?\r\nHint: What is 29.4% of 500?<\/li>\r\n \t
  2. What is the null hypothesis value of [latex] p [\/latex]?<\/li>\r\n \t
  3. In this example, we meet the following conditions for a one-sample z-test for\u00a0 proportions.\r\n
    \r\n\r\nConditions for One-Sample Z-Test for Proportions *MISSING LATEX*\r\n
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    1. Large Counts: Check that 10 and\u00a0 10.<\/li>\r\n \t
    2. Random Samples\/Assignment: Check that the samples are random samples.<\/li>\r\n \t
    3. 10% Population Size: Check that the sample size, , is less than 10% of the population size, : 0.10.<\/li>\r\n<\/ol>\r\n<\/div>\r\nThus, we can use the normal distribution to model the values of the sample proportion that would occur if the null hypothesis is true.\r\n\r\nWhat are the mean and standard deviation of the null distribution? Round to the nearest ten thousandth.\r\nHint: Recall that the mean of all sample proportions is calculated by\u00a0[latex] \\mu= p [\/latex] and the standard deviation of the sample proportions is [latex] \\sigma =\\sqrt{\\frac{1-p}{n}} [\/latex'<\/li>\r\n \t
    4. Consider the sampling distribution of the sample proportion. In In-Class Activity 11.B, we used the Empirical Rule to determine if a test statistic was \u201cunusual.\u201dUsing the Empirical Rule, what value(s) of the test statistic would be \u201cunusual?\u201dHint: When is a z-score considered \u201cunusual?\u201d<\/li>\r\n<\/ol>\r\n<\/div>\r\nBased on the answers to Parts A and B, we would expect about 29.5% (147) of the\u00a0 claims to the FTC in Florida to be because of identity theft. What if 29.6% (148) were\u00a0 due to identity theft? Or 29.8% (149)?\r\n\r\nAt what point does the number seem unusual? That is, at what point does it appear that\u00a0 Florida identity theft complaints surpass that of the national percentage? How do we\u00a0 measure that?\r\n\r\nIn statistical testing, we define the P-value as the probability of obtaining a test statistic\u00a0 at least as extreme (in the direction of the alternative hypothesis) as the one that is actually seen if the null hypothesis is true. That is, a P-value answers the question:\r\n\r\n\u201cHow unlikely is the sample data given the null hypothesis is true?\u201d\r\n\r\nIt is important to remember that a P-value is a probability, which means that it is a number between 0 and 1.\r\n