Confidence Intervals for One Mean: Interpreting the Interval

[@ukasz109]

Best explanation ever!!! 😊

[@jbstatistics]

Great! I'm glad to be of help Arif.

[@lucymartinez4066]

Thank for giving various examples of how to express the result. I have not seen anyone else do that. We are asked to do this in exams but we are often not taught how to do this. Thanks! It is great you explained it and emphasized it. Thanks!

[@barjotmundi4210]

You have no idea how much this video has helped me. I have been struggling to find a proper explanation of this concept for hours. Your video has helped me a lot!! Everything is so clear. GOD BLESS YOU!!!

[@kuchabhi]

Such a wonder set of videos! Kudos!

[@James196007]

You've left out the most common mistake with confidence intervals, which is the assumption that once you've calculated it the 95% probability will always hold good. "If the interval fails to contain the expected parameter..." then you are looking at an interval selected at random from a subset, not from the full set, and the probability will be different. Normally it will actually be 0%.

[@nayanvats3424]

Amazing clarity :)

[@michipichu]

Woah i've never understood this before, and i've taken 3 stats courses. I want to share this with everyone I know now hahah

[@atlantis8206]

I am Jay and I am from South korea, leaning statistic Thank you Mr. Your lesson really helpes and I never take this kind of amzing lesson before. Really appreciate! I have a question, if I choose 90% or 67% confidence interval, what detailed interpretation shoud be??? Shoud I say : “Sure 95% that~~~”? Really hope I can get answer from you. Thanks

[@kewuiinbolanosgomez5622]

awesomeee, good job bro thanks for al the effort in your videos

[@jbstatistics]

I'm glad to be of help!

[@lingkejiang9244]

Hi, you are such a great teacher in explaining the concepts of statistics! Thank you very much for making these videos, they have literally saved my statistics exams one after the another. Can I translate your videos into Chinese, and post them on another video site, , with your copyrights preserved?

[@sann5146]

In your example at the end at around 5:15, isn't it the case though that the population under consideration is the population of female students at the university? In which case the first interpretation is correct? Or population is taken to be some abstract population of people in general?

[@jbstatistics]

It's a confidence interval for the population *mean*, and so the interpretation of the interval must relate to that mean. The interval tells us pretty much nothing about the *percentage* of population values that would lie in the interval.

[@denisleo9069]

Hello, Thank you for all you ve done ! This is really clear ! First question : Why we cannot do a confidence interval on a statistic. (the rule of 3 sigma is false ?) I mean for a normal distribution, the probably is higher that i can find an observation next to the mean ... ? Here is the second question : I have n observations from a sample. The n observations are normally distributed. I would like to know what would be the distribution of the population. I would actually know what would be the probabality that i can found an observation into an interval. For this, I estimated the mean of the population (t distribution) from the sample. I get a confidence interval (95 %) for the mean. I did the same for the standard deviation (chi 2 distribution) and then ... I took the maximum standard deviation from the confidence interval (95%) of the standard deviation (which is a worst case scenario) and i plotted 2 normal distributions with the minimum and maximum mean from the confidence interval of the mean. And the question was what can i say with this 2 plots, how can i define that 95 % of the observations would be located between this minimum limit and this maximum limit ? How can i define the limits ? Thank you very much and have a nice day ! :D

[@Foram-mz9uo]

If I draw out a random sample of 28 females with a sample mean x bar from the obv, there is a 5 % chance that the Confidence interval does not contain the Population mean. right? assuming CI of 95%

[@candycandy319]

you're legend

[@zhideliang]

So, for a 99% confidence interval, visually, do you increase the width of each interval, so that now, 99% of those intervals will capture the population mean ?

[@jbstatistics]

Yes.

[@DarinBrownMath]

Good video, but you left out the most common incorrect interpretation: saying that there is a "95% probability" that the population mean lies within a particular constructed confidence interval...

[@jbstatistics]

Hi Darin. I'm of the belief that making a major point of that notion in an applied introductory statistics course does more harm than good. In this video I do make a point of the fact that the population mean is a fixed value that does not vary from sample to sample, and the sample mean varies from sample to sample about this fixed value. I think it makes more sense to discuss it in this way, rather than focus on the notion that, for technical reasons, we can't state "there is a 95% probability that mu lies in the interval." I personally don't care a great deal what the source of the uncertainty is. (Is a flipped coin still in the air, or is it on the ground but unseen?) That said, in a lecture setting with a little more time, I do discuss this notion in greater detail and discuss why I don't make as big a point of it as some others do. Opinions will differ, of course. Cheers.

[@DarinBrownMath]

I understand your reasons for not wanting to get into it much. It's a pretty subtle point that depends on understanding an interval as a random entity, which takes some mathematical maturity to appreciate. When I teach lower-division stats, I strongly emphasize the long-term success frequency of constructed confidence intervals. But I also mention something like, "We can say there's a 95% probability the mean lies in the interval before we construct it, but not after." What gets me is that lots of people who teach stats in other departments who aren't mathematicians do teach it wrong, and those people pass along that misinterpretation... all the way to places like the Khan Academy, where just about every video is wrong... What are you going to do?... :)

[@DarinBrownMath]

Thanks for your videos, btw. I recommend your channel to my students!

[@jbstatistics]

Darin Brown Yes, it's extremely problematic that so many resources contain fundamental errors. In most cases, students can't possibly be expected to figure out that a seemingly trusted source is completely wrong. I've come to realize over the past year or so just how pervasive the problem is. I, like everybody else, make mistakes from time to time and do almost nothing perfectly, but I have been astounded by the egregious errors in many online resources. I could show you my long list of fundamental errors I've seen in statistics MOOCs, but if you're anything like me it would make you very sad. And angry. If you ever catch me making an error, please do let me know -- I don't want to be part of the problem.

[@jbstatistics]

Darin Brown You are very welcome! I hope your students find some of my videos helpful.

[@citricmelon]

goat

[@DanGM123]

capture mew