statistics 4 problems IF YOU CANT DO AT 10 DONT WASTE TIME BIDDING I DONT NEED SLOGANS

Homework Assignment # 5 Due at the beginning of class on Tuesday (12/5)

Instructions:

- Do the following four problems by hand. Show all work. - Make sure you staple (or paperclip) your homework. Loose homework will

NOT be graded. - There is no need to attach the homework questions Assigned problems:

Problem 1: A sample of 50 homes in a subdivision showed that 24 were ranch style.

a. Verify that the sample proportion of ranch style homes is normally distributed.

b. Construct a 95% confidence interval for the true population proportion of ranch style homes.

Problem 2: Monthly apartment rent is a normally distributed random variable. A sample of 12 monthly rents has a mean of $812.5 with a variance of 6148.12.

a. Estimate μ using an 80% confidence interval. b. Can you conclude that the true mean monthly rent is different than

$800? Explain why. c. Given the same information, would an 90% confidence interval be

narrower or wider than the interval in part (a)? Explain why.

Problem 3: Patients’ wait time at a hospital’s emergency room is a normally distributed random variable. A sample of 40 patients showed a mean wait time of 52.74 minutes with a standard deviation of 13.21 minutes.

a. Construct a 95% confidence interval for the population standard deviation of wait time.

b. Can you conclude that the population standard deviation is different than 18? Explain why.

Problem 4: A random sample of 100 items is drawn from a normal population whose standard deviation is 50. The sample mean is 850.

a. Estimate μ using an 88% confidence interval b. Describe how the confidence interval changes as n increases. Explain

why.