Describe another way you can perform a hypothesis test for the...

Question

Describe another way you can perform a hypothesis test for the difference between the means of two populations using independent samples with and known that does not use rejection regions.

Accepted Answer

Hello, everyone, let's take a look at this question together. How can you test a hypothesis about the difference between two independent population means with known standard deviations without using rejection regions? Is it answer choice A, use the pulled sample variants and conduct an F test to compare the population means. Answer choice B, use a confidence interval or the difference in means to determine if the hypothesized difference is. Answer choice C, perform a paired sample T test since the populations are independent, or answer choice D, use the sample standard deviations to estimate the test statistic and compare it to the chi square distribution. So, in order to solve this question, we have to recall what we have learned about testing a hypothesis about the difference between two independent population means with known standard deviations, without using rejection regions. And to solve this problem, we must first evaluate each option to determine which answer choice is correct, starting with Answer choice A, which says use the pulled sample variants and conduct an F test to compare the population means. Well, we know that the F test is used for comparing variances and not means, as well as we do not use pooled variants when population standard deviations are known. Therefore, answer choice A is incorrect. Then we have answer choice B, which says use a confidence interval or the difference in means to determine if the hypothesized difference is plausible. Well, we can identify that answer choice B provides a valid alternative to using rejection regions as you compute the confidence interval or. Population means 1, subtracted by population means 2, using the known standard deviations, and then you can identify if the hypothesized difference, which is often zero, is not in the interval, you would reject the null hypothesis, but if it is in the interval, you would then fail to reject. the null hypothesis. So based on our evaluation of answer choice B, we can identify that option B does in fact provide a method for testing a hypothesis about the difference between two independent population means with known standard deviations without using rejection regions. Therefore, answer choice B is the correct answer. And we know that all other answer choices are incorrect, as answer choice C, which says perform a paired sample T test since the populations are independent, we know is incorrect, as paired sample T tests are for dependent or matched samples and not independent ones, so answer choice C is incorrect, and then answer choice D, which says use the sample standard. Deviations to estimate the test statistic and compare it to the chi square distribution, we know is also incorrect, as this applies to testing variances and not means, and also chi square tests are not used to test for differences in population means. Therefore, only answer choice B is the correct answer. I hope you found this video to be helpful. Thank you and goodbye.

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