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Hypothesis Testing about a Populatiin Proportion (1)

Hypothesis Testing about a Populatiin Proportion (1) - 184...

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Hypothesis Testing about a Population Proportion, p Just as we conducted hypothesis tests for a population mean, µ , we can conduct hypothesis tests for a population proportion, p . The three possible setups for a test of hypothesis about p are as follows: 0 0 1 0 : : H p p H p p < 0 0 1 0 : : H p p H p p 0 0 1 0 : : H p p H p p = Lower-tailed test upper-tailed test two-tailed test Where 0 p denotes a hypothesized value for the population proportion (such as 0.10, or 0.64, etc.) When the null hypothesis is true, the distribution of the point estimate for p is: ( 29 ( 29 0 0 0 1 p p p p N with E p p and n σ - = = : . We should, of course, check to see if p is approximately normal. To do this, we use the same test that we used in Chapter 7. That is, check to see if: 0 5 np and also that ( 29 0 1 5 n p - . If the conditions for normality are met, then the following quantity is a standard normal, or “z-score”. 0 p p p z σ - = . 184
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We can conduct our hypothesis tests for p using either the p-value approach or the critical value approach . Recall that there are three steps to the p-value approach: Step 1 . State the null and alternative hypotheses. Step 2 . Compute the p-value. That is, compute the probability of observing sample results as contrary or more contrary to the null hypothesis as what you observed in your sample. Step 3 . Decide whether to accept or reject the null by comparing the p-value to α . If the p-value is less than α, reject the null. Otherwise, can not reject the null. Recall that there are five steps to the critical value approach. Step 1. State the null and alternative hypotheses. Step 2. State the critical value of the test statistic. Step 3. State your decision rule. The DR depends on the critical value of your test statistic, and whether you are conducting a two- tailed, lower-tailed or upper-tailed test. Step 4. Compute the calculated value of your test statistic. Step 5.
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