MCEN 3047: Data Analysis and Experimental Methods

Homework 5

These problems can be solved by hand or using MATLAB.

1. The American Fisheries Society is interested in the effect of mercury contamination on largemouth bass in Florida lakes. A sample of 53 fish were captured and the mercury concentration in the muscle tissue was measured (in ppm). The average mercury concentration of the sample is 0.525 ppm with a standard deviation of 0.348 ppm.

a. Find a 95% confidence interval for the mercury concentration in all largemouth bass in Florida lakes.

b. Find a 99% confidence interval for the mercury concentration in all largemouth bass in Florida lakes.

c. An AFS scientist claims that the mercury concentration is between 0.45 and 0.60 ppm. With what level of confidence can this statement be made?

2. The Charpy V-notch test is an ASTM standard test for measuring impact energy and is often used to determine whether or not a material experiences a ductile-to-brittle transition with decreasing temperature (see https://www.youtube.com/watch?v=tpGhqQvftAo for more details). Ten measurements of impact energy on specimens of A238 steel at 60 ^oC are as follows: 64.1, 64.7, 64.5, 64.6, 64.5, 64.3, 64.6, 64.8, 64.2, and 64.3 J.

a. Use the Student’s t distribution to find a 95% confidence interval for the impact energy of A238 steel at 60 ^oC.

b. Use the Student’s t distribution to find a 98% confidence interval for the impact energy of A238 steel at 60 ^oC.

3. You’re the manager of the canning line at Avery Brewing Company. When the machines are operating properly, at least 12 ounces of beer is added to each can. A sample of 40 beers from the line yields a mean of 12.05 ounces with a standard deviation of 0.2 ounces. Do you think the canning line is operating properly?

4. You’re a new hire at Medtronic working on the Endo StitchTM suturing device (https://hcpresources.medtronic.com/the-endo-stitch-suturing-device/). Currently, the grip force required to open and close the device is 20 N. Another new hire that graduated from Colorado School of Mines, who has been trying to one-up you to gain favor with your supervisor, suggests using a different bearing in the handle assembly and claims it will reduce the grip force required to operate the device. You stay late one night and modify six devices with the suggested bearing. You test the force required to operate the modified devices. Your measurements (in N) are: 19.5, 18, 20, 19, 21, 22.

Do you think the modification will reduce the grip force required to operate the device? What will you tell your supervisor?

5. You’re curious if vehicle wheelbase affects the time it takes to parallel park a car. You set up an experiment where 50 people are timed while they parallel park two different cars: one with a short wheelbase and the other with a long wheelbase. The results of the experiment yield an average park time for the short wheelbase car of 32 seconds with a standard deviation of 8 seconds. The average park time for the long wheelbase car is 37 seconds with a standard deviation of 7 seconds. Can you conclude that the time it takes to park a short wheelbase car is less than the time it takes to park a long wheelbase car?