Intro to Confidence Intervals for One Mean (Sigma Known)
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- Опубліковано 5 жов 2024
- An introduction to confidence intervals for the population mean mu. These methods are appropriate when we are sampling from a normally distributed population, where the population standard deviation sigma is known. When the population standard deviation is not known, as is usually the case, we need to use a slightly different method (a method based on the t distribution).
The 2D:4D ratio data (from the right hand) is simulated data with the same summary statistics as found in:
Stevenson et al. (2007). Attention Deficit/Hyperactivity Disorder (ADHD) Symptoms and Digit Ratios in a College Sample. American Journal of Human Biology. 19:41-50.
For those that use R, here is the R code to find the values given in the video:
To find the value of a standard normal random variable that has an area of 0.025 to the left,
qnorm(.025)
[1] -1.959964
To find the value of a standard normal random variable that has an area of 0.025 to the right,
qnorm(.975)
[1] 1.959964
To find the value of a standard normal random variable that has an area of 0.05 to the left,
qnorm(.05)
[1] -1.644854
To find the value of a standard normal random variable that has an area of 0.05 to the right,
qnorm(.95)
[1] 1.644854
thank you for making straightforward videos without trying to be cool or talking to me like I'm five years old
You are very welcome.
The only video that has helped me truly understand this subject. Khan academy talks too much and goes off topic. This was very helpful, thank you.
these 8 year old free videos are making things much much clearer than the colleges we pay thousands of dollars for!
Thanks! I built them to stand the test of time :)
I'm so grateful for all the videos you made. You literally save me from the stats final which is driving me crazy
out of all the math videos I've gone through for the past hour, your channel is
THE BEST!
definitely subscribed! Keep up the awesome work! I'm so gonna refer this channel to my classmates.
Thanks!
This guy just got me an A on my statistic exam! Thanks bro!
You are welcome Mohamed. I'm glad you did well on your exam!
He is awesome
Can't say whether your voice or your explanation is turning me on more. Great Job on the videos. Thank you.
Well, I haven't had a compliment like that before -- thanks!
So organized and straightforward, thank you. Professors dont know how to be concise like you!
I've just come across this channel to brush up on stats. I don't think I've ever seen so many thank you comments as I have here.
You have no idea at how much your videos have helped me. I have a test tomorrow and I was really confused on confidence interval! Thank you.
You are very welcome Tracy. I hope your test went well!
Amazing video, can't believe it's 8 years old. Thank you.
Great explanation. Thank you for taking time to make those videos that I am sure help tremendously students all around the world. Keep up the good work!
Hi Sangam. Thanks for the kind words. I'll definitely be adding more videos in the not-too-distant future. Cheers.
Thank you for breaking these concepts down in ways that can actually be understood rather than memorized.
You are very welcome!
Dude, I don't know if that is your real voice put it is absolutely perfect for instructional videos.
Thanks Tonia! That is indeed simply me talking, using my regular voice. Some like it, some don't :)
You are very welcome! And thanks for the compliment!
Extraordinary.. I was a little bit confused about these concepts before seeing your videos.. Wonderful explanation with very good examples 👍 Everything makes complete sense now..
Khan Academy makes very long video, and often goes off topic, which wastes a lot of time
but jbstatistics goes straight to the point, doesn't waste time on anything else
and makes short but very beautifully explained videos
ThankYou jbstatistics
I wholeheartedly agree with everything you state here :) Thanks for the kind words.
I have been watched many videos for CI but this one can help me lot more better , Thanks bro ...
I'm studying statistics at university and this is so helpful! THANK YOU
I'm glad to be of help!
thank you for this video, you saved my brain from overheating today
I hate statistics. I decided to take Stats and Calc I instead of taking Calc I and Calc II. I thought "Oh this should be a little easier." It's not. This is far worse than Calc I or Calc II. I have no patience for these graphs, Z charts, or ConnectMath's rigid answer keys. I can't get 5 minutes into my homework without wanting to punch a hole through my monitor, burn the internet, or concede to flipping burgers the rest of my life. I'm out of withdrawals for my classes so I'm stuck with it till the end. All that said, your video is a MILLION times better than my text book, or ConnectMath. Thank you.
You explained this perfectly!!!! Thank you so much😭😭😭❤️
I am really grateful for this video! It is really helpful to my learning. Thank you so much! And a late Thanksgiving greeting hehehe!
Finally I understand what the confidence intervals and alpha mean!! THAAAAANKS ALOT MAN
You are amazing, I would appreciate it if you told me how I can find the list of your posted videos. I love the way you teach
جداً أفدتني
شكراً لك
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I found your videos very helpful
thanks so much!
Great tutorial! I was so confused and this cleared everything up! Thanks for helping out this journalism student haha!!! I appreciate the help!
Thank you so much for these videos
You will have the credit, sir, for my pass of stat final tmr.
straightforward very clear best so far
Thanks!
ITS 2024, and i still watching this best video
Who is this Zed character and with 95% confidence, where can I meet him?
I can't figure out how you knew that z.025 was equal to 1.96. What table is that found in?
You have to look for 1.96 in the table 'Areas under the normal curve', the table that you use for normal distribution.
As the tail is 0.025. You have to talk half the area of the total curve (1/2 = 0.5)
Then, 0.5 - 0.025 = 0.4750, to get half of the blue shaded area.
After you have gotten 0.4750, you have to find this value in the normal curve table. When you find this values, you see that the value that corresponds to this value are 1.9 and 0.6
Therefore, 1.9 + 0.6 = 1.96!
Hope I've explained it well.
Cheers!
@@sharminmanocha3938 Thanks so much Sharmin, you helped me a lot
You articulate so well and your videos are so well organized, I almost want to think you are a program. are you?
thies2us Hey is it possible u can help me on how u get the z value (1.96 for 95% etc.)
adsonkool find a z table like faculty.elgin.edu/dkernler/statistics/ch07/images/z-table.gif and then look for the value in this case it is 0.025, (because .05 is the remainder of 1-.95) so then .05/2 for the lower and upper tail) and you should see it is equal to -1.96 if you look at the vertical and horizontal z axis. when u do lots of examples you will realise that all different confidence levels all have the same z value for each example, so as soon as u see 95% confidence level you will know it is 1.96 etc :)
This is awesome, and Thank You so much!
One help needed though..if possible, could you please include a link that explains about the box plot and quantile plot used to determine if the sample data is from normally distributed population.
This is gold man! Thanks for this!
You are very welcome!
note to self: confidnece internal : how close is the determined parameter to the actual parameter (ex. mean, standard dev)
So helpful.
Glad to be of help!
He sounds just like the NHL commentator which made learning Statistics 10x more appealing
I'm glad you liked it!
Why acceptance region should take in the middle
Such a great video!! Thanks from Sweden!
Thanks! And you're welcome!
Great explanations! Thank you very much!
Thanks for saving me during my finals
I'm glad to be of help!
I'm so happy I found your videos, you are saving my ass homie
Amazing. Great video!
this was very helpful. thank you
You are very welcome!
You just enlightened me.
I'm glad to be of help!
Very helpful - thanks!
may peace be upon you ! .from my heart
u r a king! thank you!!!!!
this was very helpful thank you very much
You are very welcome.
vids are really concise and clear.You should be our prof lol...
Thanks for the compliment!
I want to know how you got -1.645. How did you read the table to get that value. This is so confusing for a beginner. You really need to show exactly how to read the table. Please respond. Thank you
That's something that would be covered long before getting to this topic. I structure my courses, as any competent instructor would, by covering the basics of the normal distribution before getting to this material. I have multiple videos on that sort of thing. Sure, I could cover that material again in this video, and treat it as a "how to answer this question if you know nothing about the subject", but that's a terrible way to learn and a waste of time for anybody already up to speed on prior material.
I give the R code for getting these values in the description, and have multiple videos on how to use a table, including this one: ua-cam.com/video/grodoLzThy4/v-deo.html
the z value for a 95% CI is 1.645 in my statistics book!
5% of the area under the standard normal curve (0.05) lies to the right of 1.645, so we could construct a 95% *one-sided* confidence interval using 1.645. But the intervals I discuss are always two-sided, so 0.05 is split evenly into the two tails and the appropriate z value is 1.96.
got it thanks!
If you knew the standard deviation of the actual population, wouldn't that mean that you know the true mean? So taking a point estimate to infer it would be pointless, right? Can someone please clarify this, it'll help me understand this a little more
It would be a very rare case where the population standard deviation is known but the population mean is unknown, and I say as much in the video. It is, however, a useful starting point. The underlying mathematics is much simpler when the population SD is known, and certain hypothesis testing topics (e.g. power calculations) are much easier to discuss and understand in that setting. Once I cover these topics for cases where sigma is known, I move on to the case where sigma is unknown, and discuss the necessary adjustments. I take that approach because I believe it all comes together in an easier to understand package.
Thank you! You make awesome content, I just subscribed!
You are very welcome!
my confidence to pass the exam is 1-95%
awesome! thank you so much
What a brilliant way of expressing complex theories. Keep it jbstatistics, well done. May the Lord of all universes shower his mercy and blessing upon you and your family
Thanks for the compliment, and for the very kind well-wishes!
Without you i would fail my exam :)
You are amazing!
Thank you sooooo much!!!
JB; can you post a link to your video where you derive this formula (as mentioned at the beginning of this video)? Please, and thank you!
I love your videos
Is it a STD of Population or the Sample in the Margin of Error formula? I see some write there Std of Sample and some like here Std of the population, that is super confusing.
man i cant thank you enough
How did you come about getting 1.645 for Z sub 0.05 @ 5:58?
+Elle Jay Yes please, HOW ?
+Sara Alqahtani If you don't yet know how to find areas and/or percentiles for standard normal random variables using the standard normal table, I have videos that may help:
Finding Areas Using the Standard Normal Table (for tables that give the area to
left of z) (6:16) (ua-cam.com/video/-UljIcq_rfc/v-deo.html)
Finding Percentiles Using the Standard Normal Table (for tables that give the area
to left of z) (7:33) (ua-cam.com/video/9KOJtiHAavE/v-deo.html)
+jbstatistics Thaaaaaaank u so so much ♡♡♡
How is RHS 'Z' called as Z0.025? Aren't the tables measuring the area from the left hand side (cumulative) ?
I understand Z0.025 is because area to right of it is 0.025 but why this notation?
It's common notation, but not universal. It would probably be a little more satisfying and intuitive to use z_(1-alpha/2) to represent this value, and some sources do so. But it's a little messier to write out. Cheers.
Thanks :)
Cheers.
I was given an exercise where the confidence level is 5%. What z-score do I take?
Super Helpful!
I'm glad to be of help!
You kinda sound like kermit the frog
Very helpful!
I'm glad to be of help!
The reason that the normal quantile quantile plot was not necessary was because of the central limit theorem right?
It's always a good idea to plot the data and have a look before doing any type of inference or other analysis. But yes, the reason the normal qq plot was not all that important for the given example was that the sample size was fairly large, so the central limit theorem tells us that the sample mean will be approximately normal in that spot.
@@jbstatistics Got it, thanks!
this good to soport to the student
I'm glad to be of help!
Sir. Why we have to take one minus Alpha percent that is 95% in the middle of the normal curve why not to right side or left side. is there any reason to take in the middle
Muchas gracias!
+Zi Gyllenhaal De nada!
how do you get the 1.645 for 90% and 1.96 on 95%? I was looking at the Z table but how you look through the table. Do I look at the rows first or the columns?
ua-cam.com/video/grodoLzThy4/v-deo.html
thank you
Where can I find the derivation of the margin of error 2:06?
this 10 mins saved me times
How do you work this if the standard deviation is not given? I have a question right now where it says sigma is known, and follows a normal distribution. n = 20, c = 96% and xbar = 65.5. How would I compute margin of error and population standard deviation?
Nick With-Seidelin The population standard deviation is a parameter, and its value cannot be found based only on the information that you've given. There must be more information given in your problem.
"The mean number of travel days per year for the outside salespeople employed by hardware distributors is to be estimated. A sample of 20 salespeople was randomly selected. Assume the number of travel days per year for the outside salespeople employed by hardware distributors follows a normal distribution with the standard deviation is known. Assume that a 96% confidence interval for the mean number of travel days per year for the outside salespeople employed by hardware distributors was constructed, and it was (60.5, 70.5). "
Nick With-Seidelin All of those values can be found from that information. You found the mean, and with that and the interval you can find the margin of error, and from that you can get the standard deviation. I'm not going to work that out for you, but the calculations are pretty straightforward.
Do you mind showing me the formulas required? I really appreciate the help so far and that would answer all my questions. I have a midterm this week and really need to figure it out. Thanks again for responding.
Nick With-Seidelin I'm not going to go further than I've gone already. I don't help with homework problems here, I just post videos to help people with statistical concepts. It's not a tough problem, so I'm sure you can think it through. Cheers.
I don't understand how u found the z value
It's a percentile of the standard normal distribution, found using software or a table. I discuss that in various places, including here: ua-cam.com/video/grodoLzThy4/v-deo.html
jbstatistics I find it thanks a lot 💞
What does alpha represent? I am taking a business stats course and as you know different books use different symbols.
(1-alpha) is the confidence level (e.g. 0.95 for a 95% interval, which would correspond to alpha = 0.05).
So you could say that you are 95% confident that “x” lies between + or - .05 of mu?
@@liamhoward2208 I discuss it in great deal in my videos, including this one and also: Confidence Intervals for One Mean: Interpreting the Interval
to the point. thanks
You are very welcome.
awesome
so when u hav CI u don need unbiased correction for mean?
I'm not sure what you're asking. The sample mean is an unbiased estimator of the population mean.
currently crying while watching this
how did he get 0.0047? PLEASE HELP A-S-A-P
It's the result of the calculation as given: 1.96*0.028/sqrt(135).
Where did that 95% come from?
from the question
how did you find 1.96
This is known.
Could you show me how to calculate "Margin of Error", please? Thank you!
I find the margin of error for the example in this video at about 8:50.
Ty
You're welcome.
god bless you
Thanks!
Paid to college but studied at jbstatistics
fucking thankyou!
beautiful. hop on patreon i got u
Thanks for the kind words!
!
My
this is really boring
Next time I'll show a puppy in the corner.
you are not explaining anything
I am though.
Thank you soo much!!!
You are very welcome Joel!