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And at a 5% significance level, the following significance test is conducted.Īs the flow chart demonstrates above, our first step is to decide what type of test we are conducting. So, independent random samples were taken from both schools, with the results stated below. However, the provost at the nearby school believed the study time was the same and wants to clear up the controversy.
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Worked Exampleįor example, imagine the college provost at one school said their students study more, on average than those at the neighboring school. Please note, that it is infrequent to have two independent samples with equal, or almost equal, variances - therefore, the formula for un-pooled variations is more readily accepted for most high school statistics courses.īut it is an important skill to learn and understand, so we will be working through several examples of when we need to pool variances and when we do not. If this F-statistic is less than or equal to the critical number, then we will pool our variances. However, with the difference of population means, we will have to check. When we found the difference of population proportions, we automatically pooled our variances. However, there is a component we must consider, if we have independent random samples where the population standard deviation is unknown – do we pool our variances? Just like we saw with one-sample means, we will either employ a z-test or t-test depending on whether or not the population standard deviation is known or unknown. And as always, the larger the sample size the more accurate our inferences will be.
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In other words, we analyze the difference between two sample means to understand the average difference between the two populations. If our parameters of interest are the population means, then the best approach is to take random samples from both populations and compare their sample means as noted on the Engineering Statistics Handbook. So how do we compare the mean of some quantitative variables for two different populations?