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# Hypotheses for a two-sample t test

AP.STATS:
VAR‑7 (EU)
,
VAR‑7.B (LO)
,
VAR‑7.B.2 (EK)
,
VAR‑7.C (LO)
,
VAR‑7.C.2 (EK)
,
VAR‑7.F (LO)
,
VAR‑7.F.1 (EK)
,
VAR‑7.G (LO)
,
VAR‑7.G.1 (EK)

## Video transcript

market researchers conducted a study comparing the salaries of managers at a large nationwide retail store the researchers obtained salary and demographic data for a random sample of managers the researchers calculated the average salary of the men in the sample and the average salary of the women in the sample they want to test if managers who are men have a higher average salary than managers who are women assume that all conditions for inference have been met which of these is the most appropriate test and alternative hypothesis and we can see they're talking about a paired t-test and a two sample t-test and then they talk about the alternative hypotheses so pause this video and try to figure this out on your own so first let's think about the difference between a paired t-test and a two sample t-test in a paired t-test we're going to construct hypotheses around a parameter for population that will often be the mean difference so we have one population so we're talking about the paired situation right over here and so let's say we say hey do do people run faster when they wear shorts or pants and so for each member of the population you could see what you would if you really had perfect information you know how fast do they run with pants and how fast are they run with shorts and then you would calculate the difference and then across the whole population you could actually get that mean a difference so the mean difference of pants - shorts and of course in order to estimate that or in order to do a hypothesis test around that you would take a sample and then you would calculate the sample mean of the difference of pants - shorts and then you would say hey assuming the null hypothesis is true you would construct some null hypothesis likely that there is no that this mean is zero and you would say hey if the null hypothesis is true that this is actually equal to zero what's the probability that I got this result if that's below your significance level then you would reject your null hypothesis and it would suggest the alternative that might be that hey maybe mean is greater than zero on the other hand a two-sample t-tests is we're thinking about two different populations for example you could be thinking about a population of men and you could be thinking about the population of women and you want to compare the means between these two say the mean salary so you have the mean salary for men and you have the mean salary for women and what you're trying to do with the hypothesis test is try to come up with some conclusions about the mean difference between these two parameters so the mean salary for men minus the mean salary for women and our null hypothesis is usually the no news here hypothesis and so in this situation our null hypothesis is that there is no difference between these means and that our alternative hypothesis in the situation that we are looking at because they want to test if managers who are men have a higher average salary if they just wanted to test that whether managers who are men have a different salary then our alternative hypothesis would look something like this where the mean of men minus the mean of women is not equal to 0 but they aren't just testing to see if the means are different they want to see if men having a higher average salary so instead of not equal to 0 there we would have greater than 0 for our alternative hypothesis so which choice is that well we're clearly in a two-sample t-tests situation and we want to do the greater than not the not equal to so we are in that choice right over there
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