- Complete a one-sample [latex]z[/latex]-test for proportions from hypotheses to conclusions.
- Use a P-value to explain the conclusions of a completed [latex]z[/latex]-test for proportions.
one-sample [latex]z[/latex]-test of proportions
- Write out the null and alternative hypotheses.
- Check the conditions for the hypothesis test. For testing a one-sample [latex]z[/latex]-test for proportions, we require:
- Large counts: Check that [latex]np\ge10[/latex] and [latex]n(1-p)\ge10[/latex].
- Random samples/assignment: Check that the sample is a random sample.
- 10% population size: Check that the sample size, [latex]n[/latex], is less than 10% of the population size, [latex]N[/latex]: [latex]n<0.10(N)[/latex]
- Calculate a test statistic.
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[latex]\text{test statistic}: z = \dfrac{\stackrel{ˆ}{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/latex] where [latex]\stackrel{ˆ}{p}[/latex] is the sample statistic and [latex]p[/latex] is the null hypothesis value.
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- Calculate a P-value.
- Compare the P-value to the significance level, [latex]\alpha[/latex], to make a decision.
Decision Conclusion If P-value [latex]\le\alpha[/latex], there is enough evidence to reject the null hypothesis. At the [latex]\alpha\times[/latex]100% significance level, the data provide convincing evidence in support of the alternative hypothesis. If P-value [latex]\gt\alpha[/latex], there is not enough evidence to reject the null hypothesis. At the [latex]\alpha\times[/latex]100% significance level, the data do not provide convincing evidence in support of the alternative hypothesis. - Write a conclusion in context (e.g., we do/do not have convincing evidence…).
Step 2: Enter the Sample Size and the # of Successes accordingly.
Step 3: Change the Type of Inference to Significance Test.
Step 4: Enter the Null value and change the Alternative accordingly.
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Try it out with the example below.