A researcher wishes to estimate the average blood alcohol concentration (BAC) for drivers involved in fatal accidents who are found to have positive BAC values. He randomly selects records from 51 such drivers in 2009 and determines the sample mean BAC to be 0.16 g/dL with a standard deviation of 0.060 g/dL. Complete parts (a) through (c) below.
(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 BAC.
A.Since the distribution of blood alcohol concentrations is not normally distributed (highly skewed right), the sample must be large so that the distribution of the sample mean will be approximately normal.
B. Since the distribution of blood alcohol concentrations is not normally distributed (highly skewed right), the sample must be large to ensure that the sample size is greater than 5% of the population.
C. Since the distribution of blood alcohol concentrations is normally distributed, the sample must be large so that the distribution of the sample mean will be approximately normal.
D. Since the distribution of blood alcohol concentrations is normally distributed, the sample must be large to ensure that the sample size is greater than 5% of the population.
(b) Determine and interpret a 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC.
(Use ascending order. Round to three decimal places as needed.)
A.The lower bound is ? and the upper bound is ?.The researcher is 10% confident that the population mean BAC is in the confidence interval for drivers involved in fatal accidents who have a positive BAC value.
B.The lower bound is ? and the upper bound is ?. The researcher is 90% confident that the population mean BAC is in the confidence interval for drivers involved in fatal accidents who have a positive BAC value.
C.The lower bound is ? and the upper bound is ?. The researcher is 90% confident that the population mean BAC is not in the confidence interval for drivers involved in fatal accidents who have a positive BAC value.
(c) All areas of the country use a BAC of 0.10 g/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.Yes, it is possible that the mean BAC is less than 0.10 g/dL, because it is possible that the true mean is not captured in the confidence interval, but it is not likely.
B.Yes, it is possible that the mean BAC is less than 0.10 g/dL, because it is possible that the true mean is not captured in the confidence interval and it is highly probable.
C.No, it is not possible that the mean BAC is less than 0.10 g/dL, because it is possible that the true mean is not captured in the confidence interval.
D.No, it is not possible that the mean BAC is less than 0.10 g/dL, because it is possible that the true mean is not captured in the confidence interval, but it is not likely.
(a) A.Since the distribution of blood alcohol concentrations is not normally distributed (highly skewed right), the sample must be large so that the distribution of the sample mean will be approximately normal.
(b) B.The lower bound is 0.146 and the upper bound is 0.174. The researcher is 90% confident that the population mean BAC is in the confidence interval for drivers involved in fatal accidents who have a positive BAC value.
(c) A.Yes, it is possible that the mean BAC is less than 0.10 g/dL, because it is possible that the true mean is not captured in the confidence interval, but it is not likely.
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