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Blood Alcohol Concentration A random sample of 51 fatal crashes in 2013 in which the driver had a positive blood alcohol concentration (BAC) from the National Highway Traffic Safety Administration results in a mean BAC of 0.167 gram per deciliter \((\mathrm{g} / \mathrm{dL})\) with a standard deviation of \(0.010 \mathrm{~g} / \mathrm{dL}\) (a) A histogram of blood alcohol concentrations in fatal accidents shows that BACs are highly skewed right. Explain why a large sample size is needed to construct a confidence interval for the mean BAC of fatal crashes with a positive \(\mathrm{BAC}\) (b) In \(2013,\) there were approximately 25,000 fatal crashes in which the driver had a positive BAC. Explain why this, along with the fact that the data were obtained using a simple random sample, satisfies the requirements for constructing a confidence interval. (c) Determine and interpret a \(90 \%\) confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC. (d) All 50 states and the District of Columbia use a BAC of \(0.08 \mathrm{~g} / \mathrm{dL}\) as the legal intoxication level. Is it possible that the mean BAC of all drivers involved in fatal accidents who are found to have positive BAC values is less than the legal intoxication level? Explain.

A random sample of 1003 adult Americans was asked, "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without (a) Obtain a point estimate for the population proportion of adult Americans who believe that televisions are a luxury they could do without. (b) Verify that the requirements for constructing a confidence interval about \(p\) are satisfied. (c) Construct and interpret a \(95 \%\) confidence interval for the population proportion of adult Americans who believe that televisions are a luxury they could do without. (d) Is it possible that a supermajority (more than \(60 \%\) ) of adult Americans believe that television is a luxury they could do without? Is it likely? (e) Use the results of part (c) to construct a \(95 \%\) confidence interval for the population proportion of adult Americans who believe that televisions are a necessity.

In a USA Today/Gallup poll, 768 of 1024 randomly selected adult Americans aged 18 or older stated that a candidate's positions on the issue of family values are extremely or very important in determining their vote for president. (a) Obtain a point estimate for the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president. (b) Verify that the requirements for constructing a confidence interval for \(p\) are satisfied. (c) Construct a \(99 \%\) confidence interval for the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president. (d) Is it possible that the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president is below \(70 \%\) ? Is this likely? (e) Use the results of part (c) to construct a \(99 \%\) confidence interval for the proportion of adult Americans aged 18 or older for which the issue of family values is not extremely or very important in determining their vote for president.

How much time do Americans spend eating or drinking? Suppose for a random sample of 1001 Americans age 15 or older, the mean amount of time spent eating or drinking per day is 1.22 hours with a standard deviation of 0.65 hour. Source: American Time Use Survey conducted by the Bureau of Labor Statistics (a) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day. (b) There are over 200 million Americans age 15 or older. Explain why this, along with the fact that the data were obtained using a random sample, satisfies the requirements for constructing a confidence interval. (c) Determine and interpret a \(95 \%\) confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day. (d) Could the interval be used to estimate the mean amount of time a 9-year- old American spends eating and drinking each day? Explain.

The following data represent the \(\mathrm{pH}\) of rain for a random sample of 12 rain dates in Tucker County, West Virginia. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. $$ \begin{array}{llllll} \hline 4.58 & 5.19 & 5.05 & 4.80 & 4.77 & 4.77 \\ \hline 5.72 & 4.75 & 5.02 & 4.74 & 4.76 & 4.56 \\ \hline \end{array} $$ (a) Determine a point estimate for the population mean \(\mathrm{pH}\) of rainwater in Tucker County. (b) Construct and interpret a \(95 \%\) confidence interval for the mean \(\mathrm{pH}\) of rainwater in Tucker County, West Virginia. (c) Construct and interpret a \(99 \%\) confidence interval for the mean \(\mathrm{pH}\) of rainwater in Tucker County, West Virginia. (d) What happens to the interval as the level of confidence is increased? Explain why this is a logical result.

In a survey conducted by the marketing agency 11 mark, 241 of 1000 adults 19 years of age or older confessed to bringing and using their cell phone every trip to the bathroom (confessions included texting and answering phone calls). (a) What is the sample in this study? What is the population of interest? (b) What is the variable of interest in this study? Is it qualitative or quantitative? (c) Based on the results of this survey, obtain a point estimate for the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom. (d) Explain why the point estimate found in part (c) is a statistic. Explain why it is a random variable. What is the source of variability in the random variable? (e) Construct and interpret a \(95 \%\) confidence interval for the population proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom. (f) What ensures that the results of this study are representative of all adults 19 years of age or older?

The Sullivan Statistics Survey I asks, "Would you be willing to pay higher taxes if the tax revenue went directly toward deficit reduction?" Treat the survey respondents as a random sample of adult Americans. Go to www.pearsonhighered.com/sullivanstats to obtain the data file SullivanSurveyI using the file format of your choice for the version of the text you are using. The column "Deficit" has survey responses. Construct and interpret a \(90 \%\) confidence interval for the proportion of adult Americans who would be willing to pay higher taxes if the revenue went directly toward deficit reduction.

The following data represent the repair cost for a low-impact collision in a simple random sample of mini- and micro-vehicles (such as the Chevrolet Aveo or Mini Cooper). $$ \begin{array}{lrlrr} \hline \$ 3148 & \$ 1758 & \$ 1071 & \$ 3345 & \$ 743 \\ \hline \$ 2057 & \$ 663 & \$ 2637 & \$ 773 & \$ 1370 \\ \hline \end{array} $$ (a) Draw a normal probability plot to determine if it is reasonable to conclude the data come from a population that is normally distributed. (b) Draw boxplot to check for outliers. (c) Construct and interpret a \(95 \%\) confidence interval for the population mean cost of repair. (d) Suppose you obtain a simple random sample of size \(n=10\) of a Mini Cooper that was in a low-impact collision and determine the cost of repair. Do you think a \(95 \%\) confidence interval would be wider or narrower? Explain.

A researcher wishes to estimate the proportion of households that have broadband Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with \(99 \%\) confidence if (a) she uses a 2009 estimate of 0.635 obtained from the National Telecommunications and Information Administration? (b) she does not use any prior estimates?

The trade volume of a stock is the number of shares traded on a given day. The following data, in millions (so that 6.16 represents 6,160,000 shares traded), represent the volume of PepsiCo stock traded for a random sample of 40 trading days in 2014. \begin{array}{llllllll} \hline 6.16 & 6.39 & 5.05 & 4.41 & 4.16 & 4.00 & 2.37 & 7.71 \\ \hline 4.98 & 4.02 & 4.95 & 4.97 & 7.54 & 6.22 & 4.84 & 7.29 \\ \hline 5.55 & 4.35 & 4.42 & 5.07 & 8.88 & 4.64 & 4.13 & 3.94 \\ \hline 4.28 & 6.69 & 3.25 & 4.80 & 7.56 & 6.96 & 6.67 & 5.04 \\ \hline 7.28 & 5.32 & 4.92 & 6.92 & 6.10 & 6.71 & 6.23 & 2.42 \\ \hline \end{array} (a) Use the data to compute a point estimate for the population mean number of shares traded per day in 2014 (b) Construct a \(95 \%\) confidence interval for the population mean number of shares traded per day in 2014 . Interpret the confidence interval. (c) A second random sample of 40 days in 2014 resulted in the data shown next. Construct another \(95 \%\) confidence interval for the population mean number of shares traded per day in 2014\. Interpret the confidence interval. $$ \begin{array}{llllrlll} \hline 6.12 & 5.73 & 6.85 & 5.00 & 4.89 & 3.79 & 5.75 & 6.04 \\ \hline 4.49 & 6.34 & 5.90 & 5.44 & 10.96 & 4.54 & 5.46 & 6.58 \\ \hline 8.57 & 3.65 & 4.52 & 7.76 & 5.27 & 4.85 & 4.81 & 6.74 \\ \hline 3.65 & 4.80 & 3.39 & 5.99 & 7.65 & 8.13 & 6.69 & 4.37 \\ \hline 6.89 & 5.08 & 8.37 & 5.68 & 4.96 & 5.14 & 7.84 & 3.71 \\ \hline \end{array} $$ (d) Explain why the confidence intervals obtained in parts (b) and (c) are different.