AP Statistics Full Unit 9 Summary Video - Inference for Slope 

You have no idea how much I appreciate this comment. I am so glad to hear that my videos changed your grade and attitude around about AP stats. I hope you get that 5 on the exam!!!

THANK YOU SIR ❤, AND HOPEFULLY I WILL​@mporinchak

Are you an international student

You're very welcome! Best of luck on the exam.

Awesome glad I can help!

So awesome that I hear I helped you turn things around. Best of luck on the exam

Thanks, will do!

Good luck!!

To keep it simple. Z interval and z test are for inference for population proportions. T interval and t test are for inference for population means.

It is hard to predict and changes every year. Once the raw scores are in usually around the top 11-13% get 5's and then down the line, so it depends on those raw scores.

If the questions is to create a confidence interval or to determine if there is significant statistical evidence you will have to do all 4 steps, name the procedure, check conditions, build the interval or find the p-value, interpret and conclude. Sometimes a question will say assume all conditions are met and therefore you wont have to check conditions.

It is so that you can treat that specific test which you are checking all of the conditions for as its own test. If you had a larger sample (because you are deriving that sample from a population) then your calculations would be just similar to the population stuff. It also helps prevent bias...... (someone has to fact check me on all of this)

When we do statistical inference it is all about the sampling distribution which is a model of all possible sample statistics from all possible samples of the same size taken from the same population. In that model, we know the possible sample statistics will vary, but they must vary independently of each other for the standard deviation (which measures that variation) to work. If we sample with replacement this is promised to us. But typically we sample without replacement which violates independence between samples. BUT this is where the 10% rule comes in. As long as the sample size is under 10% of the population, yes we are still technically violating independence, but the change is negligible so we don't worry about. Hence why we check the 10% condition. Now if the problem is experiment based with random assignment of subjects to groups we naturally have independence and do not have to check this condition. Hope that helps!

@@mporinchak this might be a bit dumb but, if a sample size is lets say exactly 10% of the population, and replacement is NOT done, wouldnt it mean that there can only be a max of 9 other samples of the same size that make up the sampling distribtuion?

I'm going to explain this using the example of choosing colored gumballs. Let's say there's 100 gumballs in 5 different colors and the probability of getting each color is 20%. All samples with this condition are without replacement, if there is replacement it's automatically independent. If you take a sample of 5 gumballs (less than 10%) then that sample doesn't affect the overall probability of getting each color enough for it to matter and we can say it is independent. If we took a sample of like 50 gumballs though, the probability of each color will change bc the mix of gumballs left in the machine would be completely different mix with different proportions of colors than what we started with so each individual observation would not be independent.

@@mambo5431 btw the 10 % condition says that the sample size must be less than or equal to population size to assume independence if sampling is done without replacement. So you could indeed assume independence if sample size is exactly equal to 10% of the population size. Hopefully that answers ur question!