LIR 832 - Lecture 3 notes

# LIR 832 - Lecture 3 notes - Hypothesis Testing LIR 832...

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1 Hypothesis Testing LIR 832 Lecture #3 January 30, 2007 Topics of the Day ± A. Our Fundamental Problem Again: Learning About Populations from Samples ± B. Basic Hypothesis Testing: One Tailed Tests Using a Z Statistic ± C. Probability and Critical Cutoff Approaches: Really the Same Thing ± D. How do we do hypothesis tests on small samples (n = 30 or less). ± E. How do we do hypothesis testing when we have information on population standard deviation? On sample standard deviations? ± F. How do we test a statement such as (two tailed test)? ± G. How do we test for differences in means of two populations? µ ≥≤ 25 6 or X = Hypothesis Testing ± Fundamental Problem: We want to know about a population which is not observed and want to use a sample to learn about the population. Our problem is that sampling variability makes sample an inexact estimator of the population. We need to come up with a method to learn about the population from samples which allows for sampling variability.

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2 Hypothesis Testing: Example ± We are considering implementing a training program which purports to improve quality and reduce the number of defects. Currently, 10 out of every 1000 parts produced are not within spec. The standard deviation of defects is 8 parts (variance is 64). The typical employee produces 1,000 parts per day ± The program costs \$1,000 per employee and we have 10,000 production employees. We are unwilling to spend \$10,000,000 for a pig in the poke. ± Instead we decide to run a pilot on 100 employees to determine whether the program is effective for our employees. The firm that does the training will do the program for free, so our only cost is lost production for the time during which employees are trained. Note that the 100 employees are a pilot or, in our terminology, a sample. Hypothesis Testing: Example ± Employees are sent to the program and then given several days under instruction to apply what they have learned to their work. We run a one day test on the employees and find that they average 8 parts per thousand. ± Defects are down, but is this really an improvement or is it simply the result of sampling variation? Could we be reasonably certain if we trained a second group of employees, or ran this same test next week, that defects would also be down? Hypothesis Testing: Example ± Abstractly, we are faced with the problem of distinguishing whether the program is effective or whether the improvement is reasonably explained by sampling variation (aka luck).
3 Hypothesis Testing: Example ± Let’s approach this as a statistical problem. We know that historically there have been 10 defects per 1000 with standard deviation of 8. So our question is, “How likely is it that we have pulled a sample of 100 employees with a mean defect rate of 8 if, in fact, the training program did not work (in other words, that the population rate of defects remains 10 per 1000)?

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## This note was uploaded on 07/25/2008 for the course LIR 832 taught by Professor Belman during the Spring '07 term at Michigan State University.

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LIR 832 - Lecture 3 notes - Hypothesis Testing LIR 832...

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