Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interval for a sample of size 308 with 246 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.

Three friends are having a debate. They recently read that on average Americans drive 16 miles each way when computing to work by car (ABC News, 2007). Friend A suspects that the mean for Colorado  residents is likely lower than the national average because the population density of Colorado increases the likelihood that people live closer to their jobs, while friend B suspects the mean for Colorado residents is likely higher than the national average. Friend C does not find either argument very convincing and instead suspects that the mean for Colorado residents is no different from the US population mean. The three friends bet a dinner at Alinea and set out to resolve the debate. Using a random sample of 20 Colorado residents, they calculate the mean for their sample to be 14.23 miles with a standard deviation of 2.34. The three friends did not pay very close attention in their statistics class, so they need your help making sense of these numbers. Compute the 95% confidence…

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Michelle, a student studying music, randomly sampled fellow music majors and asked whether they listen to music while they study. The resulting confidence interval for the proportion of music students who listen to music while studying is (0.09, 0.26). What is the margin of error?