Homework 6 - Due Oct 30
You may work in groups, but the homework must be done individually.
Hutchinson-Gilford progeria syndrome (HGPS) is an extremely rare genetic disorder that causes children to age prematurely. The disease affects an estimated one in 18 million people. Assume that you have developed a test for newborns that is 99% accurate (for both patients with and without the disease). What is the chance that a patient with a positive test result for HGPS actually has it?
Assume the probability of having the seasonal flu is 10%. Assume that you have a test that is 99% accurate (for both patients with and without the disease). What is the chance that a patient with a positive test result for the flu actually has it?
You are in charge of the production line at a company that makes coronary stents. As production engineer, you have measured all of the stent lengths for an entire production run and know the population average (\(\mu=23.7\) mm) and standard deviation (\(\sigma=0.95\) mm). Assume a normal distribution.
a. Find the probability that a randomly chosen stent has a length of (1) less than 20 mm, (2) between 21 and 22 mm, (3) between 21 and 25 mm, and (4) greater than 25 mm.
b. Find the following percentiles for stent length: (1) 1st, (2) 10th, (3) 50th, and (4) 95th.
A biomedical engineer on the staff of a physical therapy research team made a sampling study to evaluate her new design for an exerciser. The device is intended to strengthen the muscles in persons suffering from chronic lower back pain. The availability of only one test device limited the number of test subjects that could be accommodated. A random sample of 12 patients was treated with the exerciser, and the mean recovery time was found to be \(\bar X = 24.7\) days with a sample standard deviation of \(s=7.6\) days.
a. Calculate the confidence interval for a 95% level of confidence.
b. Calculate the confidence interval for a 99% level of confidence.