Minitab v13 -
Hypothesis Testing: Dichotomous Variables

Binomial Test . The Minitab Project is available.

First we need to generate numbers representing the different possible outcomes. Use the "Simple Set of Numbers..." command off of the "Calc, Make Patterned Data" menu. While for our example, we could easily type in the 11 numbers, the procedure demonstrated would work just as easily for hundreds of numbers.

That will take you to the following dialog box:

I had already named C1 as possib in the Minitab worksheet. Type possib as the place to "Store patterned data in:". Then type 0 as the first value and 10 as the last (making sure the rest of the boxes have a one. This will generate the numbers 0 - 10 for the possib variable. Note that this is 0-10, not 1-10. Now we can generate the binomial distribution. Use the "Binomial..." command off of the "Calc, Probability Distributions" menu. That is:

That will take you to the following dialog box:

Make sure the "Probability" radio button is checked. Then type in 10 for "Number of trials:" and .5 for the "Probability of success:". Lastly, type or click the "Input column" as possib. The output will look like this:

 Probability Density Function Binomial with n = 10 and p = 0.500000      x      P( X = x )   0.00      0.0010   1.00      0.0098   2.00      0.0439   3.00      0.1172   4.00      0.2051   5.00      0.2461   6.00      0.2051   7.00      0.1172   8.00      0.0439   9.00      0.0098  10.00      0.0010

So this is the binomial distribution. (Probabilities shown in color are relevant to the example given in lecture.) For our purposes though, it would have been even better to choose the "Cumulative probability" radio button in the dialog box above which would have given:

 Cumulative Distribution Function Binomial with n = 10 and p = 0.500000    x    P( X <= x )   0.00      0.0010   1.00      0.0107   2.00      0.0547   3.00      0.1719   4.00      0.3770   5.00      0.6230   6.00      0.8281   7.00      0.9453   8.00      0.9893   9.00      0.9990  10.00      1.0000