USES AND ABUSES Statistics in the Real World 336 CHAPTER 6 Confidence Intervals EXERCISES 1. Unrepresentative Samples Find an example of a survey that is reported in a newspaper, in a magazine, or on a website. Describe different ways that the sample could have been unrepresentative of the population. 2. Biased Survey Questions Find an example of a survey that is reported in a newspaper, in a magazine, or on a website. Describe different ways that the survey questions could have been biased. 3. Misinterpreted Polls Determine whether each state election poll below was misleading. Assume the margin of error is 4% for each poll. (a) Michigan poll leader: Clinton by 3.4%; Election winner: Trump by 0.3% (b) Wisconsin poll leader: Clinton by 6.5%; Election winner: Trump by 0.7% Uses By now, you know that complete information about population parameters is often not available. The techniques of this chapter can be used to make interval estimates of these parameters so that you can make informed decisions. From what you learned in this chapter, you know that point estimates (sample statistics) of population parameters are usually close but rarely equal to the actual values of the parameters they are estimating. Remembering this can help you make good decisions in your career and in everyday life. For instance, the results of a survey tell you that 52% of registered voters plan to vote in favor of the rezoning of a portion of a town from residential to commercial use. You know that this is only a point estimate of the actual proportion that will vote in favor of rezoning. If the margin of error is 3%, then the interval estimate is 0.49 6 p 6 0.55 and it is possible that the item will not receive a majority vote. Abuses Unrepresentative Samples There are many ways that surveys can result in incorrect predictions. When you read the results of a survey, remember to question the sample size, the sampling technique, and the questions asked. For instance, you want to know the proportion of people who will vote in favor of rezoning. From the diagram at the left, you can see that even when your sample is large enough, it may not consist of people who are likely to vote. Biased Survey Questions In surveys, it is also important to analyze the wording of the questions. For instance, the question about rezoning might be presented as: “Knowing that rezoning will result in more businesses contributing to school taxes, would you support the rezoning?” Misinterpreted Polls Some political pundits and voters vowed never to trust polls again after they failed to predict Donald Trump’s win over Hillary Clinton in the 2016 U.S. presidential election. However, nationwide polls the week of the election were only off by about 1%—the polls showed Clinton ahead by about 3% and she ended up ahead in votes by about 2%. Many state polls were inaccurate, most of them in the same direction, with Trump receiving up to 10% more of the vote than expected in some states. This was enough to give him the majority of electoral votes and the presidency. Analysts had a variety of theories why some polls underpredicted Trump’s performance in 2016 and to a lesser extent in 2020. Likely voters Registered voters People sampled
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