Binomial Distribution Test

Based on Margin of Error

Copying bnmerr

bnmerr is similar to the binom program. The sample size is based on:

bnmerr has four parameters:

Example of how to run the program.

      bnmerr 95.0 0.01 17 0.6

In this example, the program calculates the sample size based on a confidence level of 95 percent that the program will have an error rate of one percent. The program makes 17 trials for success at a 60 percent success rate, and then prints the probability distribution, the standard deviation, and the chi-square test.

The Chi-square number should fit within the Range 95 percent of the time.


References

The calculation of probabilities for the binomial distribution is based on the following book:

Lincoln L. Chao
Statistics for Management
2nd Edition
Palo Alto: The Scientific Press, 1984
Chapter 7, Discrete Probability Distributions
Section 2, Binomial Distribution
Chapter 9, Statistical Estimation
Section 4, Determination of Sample Size

Lincoln L. Chao published his book while at California State University, Long Beach.

The chi-square test is similar to:

Chapter 12, Chi-square Tests
Section 3, Testing for Goodness of Fit
Formula 12-3
Example 12-4

In Table 12-3, each category in the chi-square test has a different expected frequency. This corresponds to the different expected frequencies for the number of successes.