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# Comparing P-value from t statistic to significance level

AP.STATS:
DAT‑3 (EU)
,
DAT‑3.E (LO)
,
DAT‑3.E.1 (EK)
,
DAT‑3.F (LO)
,
DAT‑3.F.1 (EK)
,
DAT‑3.F.2 (EK)

## Video transcript

Jude was curious if the automated machine at his restaurant was filling drinks with the proper amount he filled a sample of 20 drinks to test his null hypothesis which is the actual population mean for how much drink there was and in the drinks per drink is 530 millilitres versus his alternative hypothesis is that the population mean is not 530 millilitres where mu is the mean filling amount the drinks in the sample contained a mean amount of 528 millilitres with a standard deviation of 4 milliliters these results produced a test statistic of T is equal to negative two point two three six and a p-value of approximately zero point zero three eight assuming the conditions for inference were met what is an appropriate conclusion at the alpha equals 0.05 significance level and they give us some choices here and like always I encourage you to pause this video and see if you can figure it out on your own all right so now let's work through this together so let's just remind ourselves what's going on so you have some population of drinks and we care about the true population mean you have a null hypothesis around it that the true mean is 530 millilitres but there's the alternative hypothesis that it's not 530 milliliters so to test your null hypothesis you take a sample in this case we had a sample of 20 drinks and using that sample you calculate a sample mean and then you also calculate a sample standard deviation they tell us through these things right over here and then using this information and actually our sample size you are able to calculate a T statistic you're able to calculate a T statistic and then using that T statistic you are able to calculate a p-value and the p-value is what is the probability of getting a result at least this extreme if we assume that the null hypothesis is true and if that probability is lower than our significance level then we say hey that's a very low probability we're going to reject our null hypothesis which would suggest our alternative so the key of this question is just to compare this p-value right over here to our significance level and as we see the p-value 0.038 is indeed less than a 0.05 and so because of this we would reject the null hypothesis we would reject the null hypothesis which would suggest the alternative that the true mean is something different than 530 milliliters and so if we look at our choices here so the first choice says reject the null hypothesis this is strong evidence that the mean filling amount is different than 530 milliliters yeah that one looks good we this suggests this is strong evidence this suggests the alternative hypothesis which is that right over there well sorry the other ones just make sure that they don't make sense so this is rejecting the null hypothesis that looks true so far this isn't enough evidence to conclude that the mean filling amount is different than 500 30 milliliters no not not the first one is definitely much stronger fail to reject the null hypothesis no we are rejecting the null hypothesis because our p-value is lower than our significance level fail to reject no weed rule that one out as well
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