p-hat 2 is the sample proportion x 2 /n 2.p-hat 1 is the sample proportion x 1 /n 1.If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms. You should have a cutoff value ready, such as 5% or 1%. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. p is the probability that the difference between the two proportions would occur if the null hypothesis is true.If the null hypothesis is true, it should be close to 0.
The first line, involving p1 and p2, is the alternative hypothesis.
In either case, it's important to understand the output of 2-PropZTest(. draw? (optional) set this to 1 if you want a graphical rather than numeric resultĪlthough you can access the 2-PropZTest( command on the home screen, via the catalog, there's no need: the 2-PropZTest(… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.alternative (optional if you don't include draw?) - determines the alternative hypothesis.n 2 - the total size of the second sample (so the sample proportion would be x 2 /n 2).x 2 - the success count in the second sample.n 1 - the total size of the first sample (so the sample proportion would be x 1 /n 1).x 1 - the success count in the first sample.The arguments to 2-PropZTest( (which must be integers, or the calculator will generate a domain error) are as follows:
However, in certain cases, our alternative hypothesis may be that one proportion is greater or less than the other. In addition to the null hypothesis, we must have an alternative hypothesis as well - usually, this is simply that the proportions are not equal. TI must have been afraid that this would be confused with the real number π, so on the calculator, "p1" and "p2" are used everywhere instead. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.Ĭommonly used notation has the letters π 1 and π 2 being used for the true population proportions (making the null hypothesis be π 1=π 2). If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the proportions are not equal. To do this, we assume that this "null hypothesis" is true, and calculate the probability that the differences between the two proportions occurred, under this assumption. The logic behind the test is as follows: we want to test the hypothesis that the proportions are equal (the null hypothesis). This test is valid for sufficiently large samples: only when the number of successes ( x in the command syntax) and the number of failures ( n- x) are both >5, for both populations. (outside the program editor, this will select the 2-PropZTest… interactive solver)Ģ-PropZTest( performs a z-test to compare two population proportions. Performs a z-test to compare two proportions.Ģ-PropZTest( x 1, n 1, x 2, n 2, //draw?//