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Current time:0:00Total duration:3:19

AP.STATS:

VAR‑7 (EU)

, VAR‑7.E (LO)

, VAR‑7.E.1 (EK)

Miriam was testing her null hypothesis that the population mean of some dataset is equal to 18 versus her alternative hypothesis is that the mean is less than 18 with a sample of 7 observations her test statistic I can never say that was T is equal to negative 1.9 assume that the conditions for inference were met what is the approximate p-value for Miriam's test so pause this video and see if you can figure this out on your own all right well I always just like to remind ourselves what's going on here before I just go ahead and calculate the p-value so there's some data set some population here and the null hypothesis is that the true mean is 18 the alternative is that it's less than 18 so to test that null hypothesis Miriam takes a sample sample size is equal to 7 from that she would calculate her sample mean and her sample standard deviation and from that she would calculate this T statistic the way she would do that or if they didn't tell us ahead of time what that was they'd say okay well we'd say the T statistic is equal to her sample mean minus the assumed mean from the null hypothesis that's what we have over here divided by and this is a mouthful our approximation of the standard error of the mean and the way we get that approximation we take our sample standard deviation and divide it by the square root of our sample size well they've calculated this ahead of time for us this is equal to negative 1.9 and so if we think about a T distribution I'll try to hand draw a rough T distribution really fast and if this is the mean of the T distribution what we are curious about because our alternative hypothesis is that the mean is less than 18 so what we care about is well what is the probability of getting a t-value that is more than 1.9 below the mean so this right over here negative 1.9 so it's this area right there and so I'm going to do this with a ti-84 at least an emulator of a ti-84 and all we have to do is we would go to second distribution and then I would use the T cumulative distribution function so let's go there that's the number six right there click enter and so my lower bound yeah I essentially wanted to be negative infinity and so we can just call that negative infinity is just approximation of negative infinity very very low number our upper bound would be negative one point nine negative one point nine and then our degrees of freedom that's our sample size minus one our sample size is seven so our degrees of freedom would be six and so there we have it and then so this would be our p-value would be approximately zero point zero five three so our p-value would be approximately zero point zero five three and then what Myriam would do is would compare this p-value to her preset significance level two alpha if this is below alpha then she would reject her null hypothesis which would suggest the alternative if this is above alpha then she would fail to reject her null hypothesis

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