347 Where You’re Going In this chapter, you will continue your study of inferential statistics. But now, instead of making an estimate about a population parameter, you will learn how to test a claim about a parameter. For instance, suppose that you work for Pew Research Center and are asked to test a claim that the proportion of U.S. adults who agree that people who play violent video games are more likely to be violent themselves is p = 0.35. To test the claim, you take a random sample of n = 2001 U.S. adults and find that 800 of them think that people who play violent video games are more likely to be violent themselves. Your sample statistic is np ≈ 0.400. Is your sample statistic different enough from the claim 1p = 0.352 to decide that the claim is false?The answer lies in the sampling distribution of sample proportions taken from a population in which p = 0.35. The figure below shows that your sample statistic is more than 4 standard errors from the claimed value. If the claim is true, then the probability of the sample statistic being 4 standard errors or more from the claimed value is extremely small. Something is wrong! If your sample was truly random, then you can conclude that the actual proportion of the adult population is not 0.35. In other words, you tested the original claim (hypothesis), and you decided to reject it. Where You’ve Been In Chapter 6, you began your study of inferential statistics. There, you learned how to form a confidence interval to estimate a population parameter, such as the proportion of people in the United States who agree with a certain statement. For instance, in a nationwide poll conducted by Pew Research Center, 2001 U.S. adults were asked whether they agreed or disagreed with the statement, “People who play violent video games are more likely to be violent themselves.” Out of those surveyed, 800 adults agreed with the statement. You have learned how to use these results to state with 95% confidence that the population proportion of U.S. adults who agree that people who play violent video games are more likely to be violent themselves is between 37.9% and 42.1%. 0.29 0.3 0.31 0.32 0.33 0.34 0.35 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 0.36 0.37 0.38 0.39 0.4 0.41 Claim p = 0.35 Sample statistic p ≈ 0.400 p z ˆ ˆ z ≈ 4.69 Sampling Distribution
RkJQdWJsaXNoZXIy NjM5ODQ=