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Minitab - Hypothesis Testing: Dichotomous Variables

Binomial Test . The Minitab Worksheet 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 = 0.5

     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. That is, if we sum the probabilities shown in burgandy, we get .022 as we did in class. For our purposes though, it would have been even better (more efficient) to choose the "Cumulative probability" radio button in the dialog box, that is:

The output will look like this:

Cumulative Distribution Function

Binomial with n = 10 and p = 0.5

   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

Now we simply double the number in burgandy to get the probability we got in lecture (within the limits of rounding error).


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