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A retailer wants to estimate the average amount spent by customers on holiday shopping. In a random sample of 50 customers, the average amount spent was $250, and the population standard deviation $\sigma$ is known to be $40. Construct and interpret an 80% confidence interval for the average amount spent by all customers.

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 an 80% confidence interval given a sample size of 51.