Advanced Math/stats

Advertisement

Expert: - 5/1/2009


Question
we got a review to for a final and i dont understand how to do this problem. If you could help me that would be great.

A tire manufacturer produces tires that have a mean life of at least 25000 miles when the production process is working properly/ Based on past experience, the standard deviation of the tires is 3500 miles and the tire life is normally distributed. The operations manager stops the production process if there is evidence that the population mean tire life is below 2500 miles. If you select a random sample of 100 tires and you are willing to have an alpha =.05 risk committing a type 1 error, compute the power of the test and probability of type 2 error if the population mean life is actually 24000 miles. What if is 24900?

If you could show me how to do the 24000 and i can use your example to do the second, that would be great.

Thanks

Answer
We are given µ = 25,000 and σ = 3,500.

It looks like the point of interest is 2,500.

For 100 tires, it will not show at all for µ is still 25,000 and now σ would be 3,500/√100 = 3,500/10 = 350.

That would put 2500 at a distance of 22,500 from the mean.
When that is divided by σ, a large number is gotten (anything over 5 is really large in the normal), so the probability is 0.

For the type 2 errors, I believe you look at the chance of acceptance given the error is true.

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scott A Wilson

Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

Experience

Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

©2012 About.com, a part of The New York Times Company. All rights reserved.