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Chapter 3: Problem 4
Proportion of registered voters in a county who voted in the last election, using data from the county voting records.
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Mix It Up for Better Learning In preparing for a test on a set of material, is it better to study one topic at a time or to study topics mixed together? In one study, \(^{13}\) a sample of fourth graders were taught four equations. Half of the children learned by studying repeated examples of one equation at a time, while the other half studied mixed problem sets that included examples of all four types of calculations grouped together. A day later, all the students were given a test on the material. The students in the mixed practice group had an average grade of \(77,\) while the students in the one-at-a-time group had an average grade of \(38 .\) What is the best estimate for the difference in the average grade between fourth-grade students who study mixed problems and those who study each equation independently? Give notation (as a difference with a minus sign) for the quantity we are trying to estimate, notation for the quantity that gives the best estimate, and the value of the best estimate. Be sure to clearly define any parameters in the context of this situation.
3.54 Number of Text Messages a Day A random sample of \(n=755\) US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages, \({ }^{25}\) with standard error about 6.1 (a) State the population and parameter of interest. Use the information from the sample to give the best estimate of the population parameter. (b) Find and interpret a \(95 \%\) confidence interval for the mean number of text messages.
Give information about the proportion of a sample that agrees with a certain statement. Use StatKey or other technology to estimate the standard error from a bootstrap distribution generated from the sample. Then use the standard error to give a \(95 \%\) confidence interval for the proportion of the population to agree with the statement. StatKey tip: Use "CI for Single Proportion" and then "Edit Data" to enter the sample information. In a random sample of 100 people, 35 agree.
Information about a sample is given. Assuming that the sampling distribution is symmetric and bell-shaped, use the information to give a \(95 \%\) confidence interval, and indicate the parameter being estimated. \(\hat{p}_{1}-\hat{p}_{2}=0.08\) and the margin of error for \(95 \%\) confidence is \(\pm 3 \%\).
Saab Sales Saab, a Swedish car manufacturer, is interested in estimating average monthly sales in the US, using the following sales figures from a sample of five months: \(^{37}\) \(\begin{array}{lll}658, & 456, & 830,\end{array}\) \(696, \quad 385\) Use StatKey or other technology to construct a bootstrap distribution and then find a \(95 \%\) confidence interval to estimate the average monthly sales in the United States. Write your results as you would present them to the CEO of Saab.
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