ENGT3040
Applied Material Science
9/6/2011
Some Random Notes on Null Hypothesis
1) Please find attached few pages (pages 418 & 419) from the Statistics Text that you used
in ENGT 3010 –Applied Statistics class. These pages describe in details the Null
Hypothesis workout on a ‘small sample tests for inferring (testing a hypothesis) about a
population MEAN value.
You do not copy these pages as is, but need to write an appendix to test your Hypothesis
in your first Lab that the mean measured density value of steel will not equal the
theoretical density of steel found in the literature.
2) Chebyshev’s Inequality:
The mean of a random variable is a measure of the center of its distribution, and the
standard deviation is a measure of the spread away from the mean value. Chebyshev’s
inequality provides a bound on the deviation of test value from its mean for a known
multiple of its standard deviation. Specifically, the probability that a random variable
differs from its mean by k times its standard deviations or more is NEVER greater than
1/k2.
P(|X - µx| ≥ kσx ) ≤ 1/k2
3) Two Pages of your Statistics text, attached as a pdf document, on an example of
hypothesis testing of a claim with ‘Small Sample data with unknown Standard deviation’
4) One side page, attached as a pdf document ‘Coffee cup Hypothesis example’, on another
example of hypothesis testing of a claim with ‘Small Sample data with known Standard
Deviation’ (This hypothesis example is from ‘Humongous Book of Statistics Problems’
book)
5) A t-distribution table for use, as a pdf file
6) You can see a normal distribution table from any statistics textbook, if you need