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# Examples thinking about power in significance tests

AP.STATS:
UNC‑5 (EU)
,
UNC‑5.C (LO)
,
UNC‑5.C.1 (EK)

## Video transcript

a significance test is going to be performed using a significance level of five hundredths suppose that the null hypothesis is actually false if the significance level was lowered to one hundredth which of the following would be true so pause this video and see if you can answer it on your own okay now let's do this together and let's see they're talking about how the probability of a type 2 error or the power or and/or the power would change so before I even look at the choices let's think about this we've talked about in previous videos that if we increase our level of significance that will increase our power and power is the probability of not making a type 2 error so that would decrease the probability of making a type 2 error but in this question we're going the other way we're decreasing the level of significance which would lower the probability of making a type 1 error but this would decrease the power it actually would increase it actually would increase the probability of making a type 2 a type 2 error and so which of these choices are consistent with that well choice A says that both the type 2 error and the power would decrease well those don't these two things don't move together if one increases the other decreases so we rule that one out choice B also has these two things moving together which can't be true if one increases the other decreases choice C the probability of a type 2 error would increase that's consistent with what we have here and the power of the test would decrease yep that's consistent with what we have here so that looks good and choice D is the opposite of that the probability of a type 2 error would decrease so this is they're talking about this scenario over here and that would have happened if they increased our significance level not decreased it so we could rule that one out as well let's do another example Asha owns a car wash and is trying to decide whether or not to purchase a vending machine so that customers can buy coffee while they wait she'll get the machine if she's convinced that more than 30 percent of our customers would buy coffee she plans on taking a random sample of n customers and asking whether or not they would buy coffee from the machine and she'll then do a significance test using alpha equals 0.05 to see if the sample proportion who say yes is significantly greater than 30% which situation below would result in the highest power for her test so again pause this video and try to answer it well before I even look at the choices we could think about what her hypotheses would be her null hypothesis is you can kind of use the status quo no no news here and that would be that the true population proportion of people who want to buy coffee is 30% and that her alternative hypothesis is that no the true population proportion the true population parameter there is greater than is greater than 30% and so if we're talking about what would result in the highest power for her test so a high power a high power means the the lowest probability of making a type 2 error and in other videos we've talked about it looks like she's dealing with the sample size and what is the true proportion of customers that would buy coffee and the sample size is under her control the true proportion isn't don't want to make it some seem like somehow you can change the true proportion in order to get a higher power you can change the sample size but the general principle is the higher the sample size the higher the power so you want a high as possible sample size and you're going to have a higher power if the true proportion is further from your hypothesis your null hypothesis proportion and so we want the highest possible n and that looks like an N of 200 which is there and there and we want a true proportion of customers that would actually buy coffee as far away as possible from our null hypothesis which once again would not be under Ash's control but you can clearly see that 50% is further that from 30 then 32 is so this one choice D is the one that looks good