7. Sampling Distributions & Confidence Intervals: Mean

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.

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

Find each probability.

(B)

A company wants to estimate the average time employees spend on a training module. 15 employees are randomly selected, & their completion times recorded. The sample of times to complete the module is normally distributed with mean 42.7 min & std. dev. 5.4 min.

(B) Should management be concerned that the training might take too long if their policy states the module should take at most 45 min? Justify your answer using your confidence interval.

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.

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

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.

Find the critical val. ($t_{\alpha \text{⁄}2}$) for each confidence interval.

(A) Confidence Level = $95\%,n=35$

Find the critical val. ($t_{\alpha \text{⁄}2}$) for each confidence interval.

(B) Confidence Level = $90\%,n=48$

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

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

Find each probability.

(A) $P(T>1.5),df=8$

A company wants to estimate the average time employees spend on a training module. 15 employees are randomly selected, & their completion times recorded. The sample of times to complete the module is normally distributed with mean 42.7 min & std. dev. 5.4 min.

(A) Make a 95% conf. int. for the true mean time to complete the training.

A nutritionist wants to estimate the average grams of protein in a brand of protein bars. She takes a random sample of 40 protein bars with $\bar{x}=210$ g & knows from prior data that $\sigma =12$. Make a 95% conf. int. for $\mu$.