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# Examples identifying Type I and Type II errors

AP.STATS:
UNC‑5 (EU)
,
UNC‑5.A (LO)
,
UNC‑5.A.1 (EK)
,
UNC‑5.A.2 (EK)

## Video transcript

we are told a large nationwide poll recently showed an unemployment rate of 9% in the United States the mayor of a local town wonders if this national result holds true for her town so she plans on taking a sample of her residents to see if the unemployment rate is significantly different than 9% in her town let P represent the unemployment rate in her town here are the hypotheses she'll use so her null hypothesis is that hey the unemployment rate in her town is the same as for the country and her alternative hypothesis is that it is not the same under which of the following conditions would the mayor commit a type 1 error so pause this video and see if you can figure it out on your own now let's work through this together so let's just remind ourselves what a type 1 error even is this is a situation where we reject the null hypothesis even though it is true reject null hypothesis even though even though our null hypothesis is true and in general if you're committing either a type 1 or a type 2 error you're doing the wrong thing you're doing something that somehow contradicts reality even though you didn't intend to and so in this case that would be reject rejecting the hypothesis that the unemployment rate is 9 percent in this town even though it actually is 9 percent in this town so let's see which of these choices match up to that she concludes the town's unemployment rate is not 9 percent when it actually is yeah this in this situation in order to conclude that the unemployment rate is not 9 percent she would have to reject the null hypothesis even though the null hypothesis is actually true even though the unemployment rate actually is 9 percent so I'm liking this choice but let's read the other ones just to make sure she concludes the town's unemployment rate is not 9 percent when it actually is not well this wouldn't be an error if the null this isn't true it's not a problem to reject it so this one wouldn't be an error she concludes the town's unemployment rate is nine percent when it actually is well once again this would not be an error this would be failing to reject the null hypothesis when the null hypothesis is actually true not an error choice D she concludes the town's unemployment rate is 9 percent when it actually is not so this is a situation where she fails to reject the null hypothesis even though the null hypothesis is not true so this one right over here this one would actually be this is an error this is an error but this is a type 2 error so one way to think about it first you say okay am i making an error am i rejecting something that's true or am i failing to reject something that's false and the rejecting something that is true that's type 1 and failing to reject something that is false that is type 2 and so with that in mind let's do another example a large university is curious if they should build another cafeteria they plan to survey a sample of their students to see if there is strong evidence that the proportion interested in a meal plan is higher than 40% in which case they will consider building a new cafeteria let P represent the proportion of students interested in a meal plan here are the hypotheses they'll use so the null hypothesis is that 40% or fewer of the students are interested in a meal plan while the alternative hypothesis is that more than 40% are interested what would be the consequence of a type 2 error in this context so once again pause this video and try to answer this for yourself okay now let's do it together let's just remind ourselves what a type two areas we just talked about it so failing failing to reject in this case our null hypothesis even even though it is false so this would be a scenario where this is false which would mean that more than 40% actually do want a meal plan but you fail to reject this so what would happen is is that you wouldn't build another cafeteria because you'd say hey no they're not that many people who are interested in the meal plan but you wouldn't but actually there are a lot of people who are interested in the meal plan and so you probably won't have enough cafeteria space and so this says they don't consider building a new cafeteria when they should yeah this is exactly right they don't consider building a new cafeteria when they shouldn't well this would just be a correct conclusion they'd consider building a new cafeteria when they shouldn't and so this is a scenario where they do reject the null hypothesis even though the null hypothesis is true so this right over here would be a type 1 error type 1 error because if they're considering building a new cafeteria that means they rejected the null hypothesis even when they shouldn't that means that the null hypothesis was true so type 1 they consider building a new cafeteria when they should well once again this wouldn't be an error at all this would be a correct conclusion this one and this one are correct conclusions this is the concert a and C are the consequences of a type 2 and a type 1 error respectively
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