Abstract #302164

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JSM 2003 Abstract #302164
Activity Number: 338
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Education
Abstract - #302164
Title: Testing for the Population Mean When Sampling from a Uniform Distribution
Author(s): Ronald L. Tracy*+
Companies: Oakland University
Address: Dept. of Economics, Rochester Hls, MI, 48309-4401,
Keywords: midrange ; reduced variance estimator ; power ; Type I error ; Type II error
Abstract:

When the underlying population is uniform it is well known that even with very small sample sizes that the sample mean is approximately normally distributed. This has been shown analytically and through simulation. Using this result, it is not uncommon to use a traditional t-test to test a hypothesis regarding the population mean mu. First, this paper shows that although not incorrect, that quite often using a standard z-test would result in increased power with no decrease in Type I error. The conditions for this result are evaluated. Second, the paper develops a test for mu using the sample midrange rather than the sample mean. It is shown that this test yields a substantial increase in power both in situations where the z-test can be used as well as in situations where the standard t-test is appropriate. These results are shown analytically and through simulation. Finally, an example is given comparing the three tests.

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