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.

A properly drawn random sample of one thousand individuals is used to estimate a population mean. The sampling error for the sample mean is roughly plus or minus what percent of the population mean (assuming a normal distribution and no prior knowledge of population standard deviation)?

If the significance level $\alpha$ is $0.10$, what is the corresponding confidence level for a confidence interval for the population mean?

Long Life? In a survey of 35 adult Americans, it was found that the mean age (in years) that people would like to live to is 87.9 with a standard deviation of 15.5. An analysis of the raw data indicates the distribution is skewed left.

b. Construct and interpret a 95% confidence interval for the mean.

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.99, n = 10

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.

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