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Chapter 7: Problem 16
Is simple random sampling usually done with or without replacement?
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According to a 2017 Gallup poll, \(80 \%\) of Americans report being afflicted by stress. Suppose a random sample of 1000 Americans is selected. a. What percentage of the sample would we expect to report being afflicted by stress? b. Verify that the conditions for the Central Limit Theorem are met. c. What is the standard error for this sample proportion? d. According to the Empirical Rule, there is a \(95 \%\) probability that the sample proportion will fall between what two values?
Statistics student Hector Porath wanted to find out whether gender and the use of turn signals when driving were independent. He made notes when driving in his truck for several weeks. He noted the gender of each person that he observed and whether he or she used the turn signal when turning or changing lanes. (In his state, the law says that you must use your turn signal when changing lanes, as well as when turning.) The data he collected are shown in the table. $$\begin{array}{|l|l|l|}\hline & \text { Men } & \text { Women } \\\\\hline \text { Turn signal } & 585 & 452 \\ \hline \text { No signal } & 351 & 155 \\\\\hline & 936 & 607 \\ \hline\end{array}$$ a. What percentage of men used turn signals, and what percentage of women used them? b. Assuming the conditions are met (although admittedly this was not a random selection), find a \(95 \%\) confidence interval for the difference in percentages. State whether the interval captures 0, and explain whether this provides evidence that the proportions of men and women who use turn signals differ in the population. c. Another student collected similar data with a smaller sample size: $$\begin{array}{|l|c|c|}\hline & \text { Men } & \text { Women } \\\\\hline \text { Turn Signal } & 59 & 45 \\ \hline \text { No Signal } & 35 & 16 \\\\\hline & 94 & 61 \\ \hline\end{array}$$ First find the percentage of men and the percentage of women who used turn signals, and then, assuming the conditions are met, find a \(95 \%\) confidence interval for the difference in percentages. State whether the interval captures 0 , and explain whether this provides evidence that the percentage of men who use turn signals differs from the percentage of women who do so. d. Are the conclusions in parts \(\mathrm{b}\) and \(\mathrm{c}\) different? Explain.
Pew Research reported that \(46 \%\) of Americans surveyed in 2016 got their news from local television. A similar survey conducted in 2017 found that \(37 \%\) of Americans got their news from local television. Assume the sample size for each poll was 1200 . a. Construct the \(95 \%\) confidence interval for the difference in the proportions of Americans who get their news from local television in 2016 and 2017 . b. Based on your interval, do you think there has been a change in the proportion of Americans who get their news from local television? Explain.
Assume your class has 30 students and you want a random sample of 10 of them. Describe how to randomly select 10 people from your class using the random number table.
According to a 2017 survey conducted by Netflix, \(46 \%\) of couples have admitted to "cheating" on their significant other by streaming a TV show ahead of their partner. Suppose a random sample of 80 Netflix subscribers is selected. a. What percentage of the sample would we expect have "cheated" on their partner? b. Verify that the conditions for the Central Limit Theorem are met. c. What is the standard error for this sample proportion? d. Complete the sentence: We expect ____ \(\%\) of streaming couples to admit to Netflix "cheating," give or take _____ \(\% .\)
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