#### Testing of Proportions

Testing a Single Proportion:

We are testing p, not the p hat. If you know the value of p, then there would be nothing to test.

All testing hypothesis is done beneath the supposition that the null hypothesis is true!

This is not enough to emphasize. The value for all population parameters in test statistics come from the null hypothesis. This is not only true for proportions; however for all the testing we are going to do.

Population proportion consists of an approximately normal distribution when both np and nq are at least 5. Keep in mind that we are approximating the binomial by using the normal, and that p we are talking about is the probability of success on single trial. The test statistic is exhibited in the box to the right.

The critical value is determined from the normal table, or from the bottom row of t-table.

The steps included in the hypothesis testing stay the same. The only thing which changes is the formula for computing the test statistic and possibly the distribution which is employed.

General Pattern:

Note that the general pattern of such test statistics is (Observed - Expected)/Standard deviation.

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