@picuberoot matched pairs is when you only have 1 sample but they are treated twice. For example, 10 men are weighed before the diet and after the diet. This is a matched pairs because there is only 1 sample involved and the results are dependent of each other. When calculating the values, make sure you subtract the before and after and use that as your data instead of using the original values given. Blocking is when you know there is something that is going to affect your results, so you state it beforehand. For example, I would block on gender when experimenting about heights because we know men tend to be taller than women.
@punctiliouseye wait what? maybe I’m wrong but I thought it was for invT you use n-1 and then for linear regression test for slope you use n-2…
I noticed a question that talks about T-distribution vs normal distribution and test statistics pop up occasionally on the AP exam:
An engineer for the Allied Steel Company has the responsibility of estimating the mean carbon content of a particular day’s steel output, using a random sample of 15 rods from that day’s output. The actual population distribution of carbon content is not known to be normal, but graphic displays of the engineer’s sample results indicate that the assumption of normality is not unreasonable. The process is newly developed, and there are no historical data on the variability of the process. In estimating this day’s mean carbon content, the primary reason the engineer should use a t-confidence interval rather than a z-confidence interval is because the engineer
(A) is estimating the population mean using the sample mean.
(B) is using the sample variance as an estimate of the population variance.
© is using data, rather than theory, to judge that the carbon content is normal.
(D) is using data from a specific day only.
(E) has a small sample, and a z-confidence interval should never be used with a small sample.
I don’t understand why the answer is B.
@picuberoot
So matched pairs can happen in 2 ways. 1) subjects are randomly split into two groups. group 1 gets treatment 1 first, and then treatment 2. Group 2 gets treatment 2 first, then treatment 1. Notice everyone gets both treatments just in different order.
The second way matched pairs can happen is that every subject is matched to another subject with similar characteristics. For example, in a study on weight loss, a female who weighs 130 lbs and is 5 ft tall could be matched to a female who weighs about the same and is about the same height. One of the subjects in the pair gets Treatment 1, and the other gets treatment 2 and effects are compared.
Blocking:
If we are testing weight loss drugs, we may realize that females and males are affected differently by drugs. Therefore, we do blocking. We split the group into males and females. In the male group, we randomly choose half of the males and give them treatment 1. The rest of the males get treatment 2. We compare results between both groups of males. In the female group, we randomly choose half of the females and give them treatment 1 and the rest get treatment 2. We compare results for both groups of females (by comparing weight loss).
Hope that helps!
@punctiliouseye isn’t it because variance is just your standard deviation squared and you use t distribution if standard deviation is unknown.
@gap725 no you use degrees of freedom n-2 for linear regression because you do not know either your alpha or beta (slope and intercept). You use Lin Reg t test on your calculator but most of the time, you are given computer output.
lmao isn’t that exactly what i said but thanks for clarifying !
@gap725 my apologizes, I did not read your response carefully; I thought you said to use n-1 for degrees of freedom for linear regression xD anyway, yes you are correct!
@jamanda I really think 15 is wrong, maybe I’m wrong haha but I strongly disagree with the answer and believe it is actually D… so can’t help with that
28. So with p=.44 you’re at .56 when looking at a normal curve. If you cut the p in half, you get p=.22. 1-.22 is .78 so that’s your upper p value and your lower is 0+.22=.22. Draw curves for these questions.
33. Find expected value. If you eliminate none, expected value is (1/5)(7) + (4/5)(0) because you have a 1/5 chance of guessing correct and a 4/5 chance of getting wrong and when you get it right, you get 7 points, and when it’s wrong, you get 0. If you eliminate 1, you get (1/4)(7)+(3/4)(0) for your expected value. For it to be to your advantage to guess, the expected value of a guess must be greater than the value for not answering (2 points) so keep on doing what I did above to find expected value until you get an expected value above 2.
40. P is .5, so you would think that he has an equal chance with either BUT, when n=10, there’s a much higher standard deviation than when n=100, so that means the likelihood of being farther from the mean and actually getting .7 is higher. (Law of Large Numbers) So basically as you get higher sample size, you get closer to the mean and deviation is more unlikely.
@stemscholar whoops I misunderstood the question… I for some reason thought it was asking about any three days in three weeks (ie not one each week, but there could be multiple checks in one week and none in another), so college boar’s answer makes sense now. Thanks
I have a question. For FRQ’s, if they ask you to perform an inferential statistic test, would you need to write out the formula for the calculations? I can try to memorize all those but if it’s not necessary I’d just be cool with being able to recognize which test to use and letting my calculator take over…
@xyx5182 Idk, I would play it safe and just put down the formula of any test you use
@xyx5182 You have to either state what test you’re doing or write down the actual formula. Ex: you can say 1 sample T Test or you can say t = xbar - myoo / sample SD
Oh that’s cool! So if I know which test to use, I can just do everything on the calculator and give an answer? thanks!!
how do you figure out the alternate hypothesis for tests
@xyx5182 correct, but to play it safe write down everything your calculator outputs (degrees of freedom, z or t, pvalue, etc, there’s no points taken off for that so why not just be safe). And be specific with your test type. For example, 2 sample t test for means, you need every part of that name to be safe.
@blaked it is usually stated in the problem. For example, it may say “bob is testing to see if polar bears exceed 300 pounds.” Your null would be u=300 and alternative would be u>300.
For matched pairs t test, do you have to define both parameters or just define the difference?
@blaked good luck.
http://media.collegeboard.com/digitalServices/pdf/ap/ap-statistics-course-description.pdf
Can somebody explain #14? How can I get r?
@AnniiT I’m pretty sure you define both parameters. It’ll be a trip memorizing all those stupid conditions tonight
Alright thanks!!