7. Sampling Distributions & Confidence Intervals: Mean

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.

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.

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.

For which of the following scenarios can you NOT create a confidence interval using the standard normal or Student 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.

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.

Fill out the table using a calculator and $n=30$.

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 each probability.

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

Find each probability.

(B)

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 $\mu$.