large sample proportion hypothesis testing

There is one formula for the test statistic in testing hypotheses about a population proportion. The test statistic follows the standard normal distribution. Either five-step procedure, critical value or \(p\)-value approach, can be used.

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The hypothesis test for a population proportion is a well-established process: Write down the null and alternative hypotheses in terms of the population proportion [latex]p[/latex]. Include appropriate units with the values of the proportion.

Standardized Test Statistic for Large Sample Hypothesis Tests Concerning a Single Population Proportion. The test statistic has the standard normal distribution.

Hypothesis Test for Proportions: Step 3 •Calculate Test Statistic, z* •The test statistic measures how different the sample proportion we have is from the null hypothesis •We calculate the z-score by assuming that is the population proportion 𝑧∗= ( − ) 1− 8

To learn how to apply the five-step test procedure for a test of hypotheses concerning a population mean when the sample size is large. To learn how to interpret the result of a test of hypotheses in the context of the original narrated situation.

In estimation we focused explicitly on techniques for one and two samples and discussed estimation for a specific parameter (e.g., the mean or proportion of a population), for differences (e.g., difference in means, the risk difference) and ratios (e.g., the relative risk and odds ratio).

Hypothesis Testing for Two-Sample Proportions. Null: \(H_0\colon p_1-p_2=0\) Conditions: \(n_1\hat{p}_1\), \(n_1(1-\hat{p}_1)\), \(n_2\hat{p}_2\), and \(n_2(1-\hat{p}_2)\) are all greater than five. Test Statistic: \(z^*=\dfrac{\hat{p}_1-\hat{p}_2-0}{\sqrt{\hat{p}^*(1-\hat{p}^*)\left(\dfrac{1}{n_1}+\dfrac{1}{n_2}\right)}}\)

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Consistency and asymptotic normality are the two fundamental large sample properties of estimators considered in this chapter. A consistent estimator 6 is one that converges in probability to the true value Q,,, i.e. 6% 8,, as the sample size n goes to infinity, for all possible true values.’