Find the critical value $t_{\frac{\alpha }{2}}$for an 80% confidence interval given a sample size of 51.

Second-Hand Smoke Refer to Data Set 15 “Passive and Active Smoke” and construct a 95% confidence interval estimates of the mean cotinine level in each of three samples: (1) people who smoke; (2) people who don’t smoke but are exposed to tobacco smoke at home or work; (3) people who don’t smoke and are not exposed to smoke. Measuring cotinine in people’s blood is the most reliable way to determine exposure to nicotine. What do the confidence intervals suggest about the effects of smoking and second-hand smoke?

Gas prices are getting more and more expensive. The average gas price, from a random sample of 100 gas stations, was $3.50. It is assumed that gas prices have a standard deviation of $0.04. Construct an 80% confidence interval for the true mean gas price in the United States.

Books get more and more expensive every semester, but the distribution of their prices is always normal. 25 randomly selected students in your school spent, on average $500 with a standard deviation of $50. Construct a 98% confidence interval for the true spending on books.

You want to purchase one of the new Altima. You randomly select 400 dealerships across the United States and find a mean of $25,000. Assume a population standard deviation of $2500. Construct and interpret a 94% confidence interval for the true mean price for the new Nissan Altima.

Find the critical value $t_{\frac{\alpha }{2}}$for a 95% confidence interval given a sample size of 6.

For which of the following scenarios can you NOT create a confidence interval using the standard normal or t-distribution?

You ask 16 people in your Statistics class what their grade is. The data appears to be distributed normally. You find a sample mean and sample standard deviation of 60 and 24, respectively. Construct and interpret a 95% confidence interval for the population mean class grade.

You want to take a trip to Paris. You randomly select 225 flights to Europe and find a mean and sample standard deviation of $1500 and $900, respectively. Construct and interpret a 95% confidence interval for the true mean price for a trip to Paris.