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Chapter 7: Problem 92
A poll on a proposition showed that we are \(99 \%\) confident that the population proportion of voters supporting it is between \(52 \%\) and \(62 \%\). Find the margin of error.
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You need to select a simple random sample of four from eight friends who will participate in a survey. Assume the friends are numbered \(1,2,3,4,5\), 6,7, and 8 . Select four friends, using the two lines of numbers in the next column from a random number table. Read off each digit, skipping any digit not assigned to one of the friends. The sampling is without replacement, meaning that you cannot select the same person twice. Write down the numbers chosen. The first person is number 7 .$$\begin{array}{lll}07033 & 75250 & 34546 \\\75298 & 33893 & 64487\end{array}$$ Which four friends are chosen?
Is simple random sampling usually done with or without replacement?
Just the Boys Refer to Exercise \(7.77\) for information. This data set records results just for the boys. $$\begin{array}{|lcc|}\hline & \text { Preschool } & \text { No Preschool } \\\\\hline \text { Grad HS } & 16 & 21 \\\\\hline \text { No Grad HS } & 16 & 18 \\\\\hline\end{array}$$ a. Find and compare the percentages that graduated for each group, descriptively. Does this suggest that preschool was linked with a higher graduation rate? b. Verify that the conditions for a two-proportion confidence interval are satisfied. c. Indicate which one of the following statements is correct. i. The interval does not capture 0 , suggesting that it is plausible that the proportions are the same. ii. The interval does not capture 0 , suggesting that it is not plausible that the proportions are the same. iii. The interval captures 0 , suggesting that it is plausible that the population proportions are the same. iv. The interval captures 0 , suggesting that it is not plausible that the population proportions are the same. d. Would a \(99 \%\) confidence interval be wider or narrower?
According to a 2017 Pew Research Center report on voting issues, \(59 \%\) of Americans feel that the everything should be done to make it easy for every citizen to vote. Suppose a random sample of 200 Americans is selected. We are interested in finding the probability that the proportion of the sample who feel with way is greater than \(55 \%\). a. Without doing any calculations, determine whether this probability will be greater than \(50 \%\) or less than \(50 \%\). Explain your reasoning. b. Calculate the probability that the sample proportion is \(55 \%\) or more.
In 2017 Pew Research Center polled 3930 adults in the United States and found that \(43 \%\) reported playing video games often on some kind of electronic device. a. Identify the population and the sample. b. What is the parameter of interest? What is the statistic?
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