For testing the difference between two population proportions, the pooled proportion estimate should be used to compute the value of the test statistic when the:Group of answer choicespopulations are normally distributed.sample sizes are large enough.null hypothesis states that the first population proportion is half of the second.null hypothesis states that the two population proportions are equal.
Question
For testing the difference between two population proportions, the pooled proportion estimate should be used to compute the value of the test statistic when the:Group of answer choicespopulations are normally distributed.sample sizes are large enough.null hypothesis states that the first population proportion is half of the second.null hypothesis states that the two population proportions are equal.
Solution
The pooled proportion estimate should be used to compute the value of the test statistic when the null hypothesis states that the two population proportions are equal.
Here's a step-by-step explanation:
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The null hypothesis is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups. In this case, the null hypothesis is stating that the two population proportions are equal.
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The pooled proportion is a way of "averaging" the proportions of two groups when you are comparing them. It is calculated by adding up the successes from both groups and dividing by the total number of trials from both groups.
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When the null hypothesis states that the two population proportions are equal, it means that we expect the same rate of success in both groups. Therefore, it makes sense to use the pooled proportion to calculate the test statistic, because the pooled proportion is based on the assumption that the two proportions are the same.
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The test statistic is then calculated using this pooled proportion. The difference between the sample proportions and the pooled proportion is calculated, and this difference is standardized by dividing by the standard error of the difference. The result is the test statistic, which follows a standard normal distribution under the null hypothesis.
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This test statistic is then compared to a critical value from the standard normal distribution to determine whether to reject the null hypothesis. If the test statistic is more extreme than the critical value, we reject the null hypothesis and conclude that there is evidence that the population proportions are not equal.
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