Z Tests for One Mean: The Rejection Region Approach
An introduction to the rejection region approach to reaching a conclusion in a Z test. This video discusses the rejection region in the context of a Z test for one mean, but the same logic holds for other Z tests.
Пікірлер: 92
Why can't all statistics teachers be like you! Your students are so lucky to have you! My teacher taught me all this too but we did it blindly in class without understanding why or how! I feel so ecstatic understanding the concept... on top of the world... my alternative hypothesis is that Indian education system sucks!
@EvilSapphireR
2 жыл бұрын
Should be the null hypothesis.
This one of the most direct and clear video I have ever seen. Straight to the point, thanks man!
You're welcome and thanks very much for the compliment! I'm just north of you, at the University of Guelph. I'm very glad you find my videos helpful. Best of luck in your courses!
I'd never imagined that I'd comment on any youtube video . I wish i could thank you in person for doing such a great job. Math would've been so much fun if only all teachers were like you. Thank you :D
I literally love you so much. So much simpler than it seems in my notes.
Woooow I digged in the whole internet for someone to explain these concepts scientifically and smoothly, and found none, but you, you are like an angle, you elaborate on the concepts so smoothly, in an extremely understandable fashion. Thank you man, thank you so much🌷🌷🌷
Thanks David! I'm currently focusing on getting a few new videos out (and a few other things). I'll soon be giving some more thought to where I'm going with all of this, and what I hope to achieve long term. Thanks for the feedback.
You are an hero. Your teaching is the best.
This comment is not only for this video but for all your videos. - I dont want to compare but in my case it happened that even after reading famous writers' textbook my understanding of many many topics are clear when I watched your videos. You are a rockstar. No one can explain better than you. Appreciate Million times
@jbstatistics
8 жыл бұрын
Thanks so much!!! I'm very glad you've found my videos helpful. All the best!
Thanks Vinayak! I'm glad you find my videos helpful.
Man, your 10-minute-video explains what my professor could not explain in two months..
cramming rn and this is ultra helpful! thanks dude :)
This is truly brilliant! Thanks a lot!!
You're welcome! Best of luck on your test.
I find you from MJ The Student Actuary. Thanks for sharing your knowledge I have really enjoyed my experience in understanding statistics from your videos - Subscribed!!
your videos are just amazing! thank you!
I studied from almost 15 videos at youtube, This is the beat content.
After working out for 2 days, at last i become success to know these boring matter. Thnx.
I think you just saved my life thank you I might cry now.
@m_riatik
3 жыл бұрын
im already crying
Best explanation of "rejection region" in youtube
You are excellent.Great explanation by a great teacher,thanks a lot :)
@jbstatistics
7 жыл бұрын
You are very welcome, and thanks for the compliment!
Your videos are awesome. You have enough material that you should consider a full Coursera or edX offering.
MAN YOU'RE THE BEST!!
@jbstatistics
7 жыл бұрын
Thanks!
what if I have a so called nested hypothesis so that my H0: is my
Dear Sir, Now i got it & cleared my concept about the hypothesis test.I am in operation field preparing for Green belt SS doing my job in a company.The course is free as it is a part of our company's strategy to train the employees to make them efficient and productive in their work culture.They have provided us bulky literature's and books and take weekly 3 hr session but i could not understanding because of job responsibility.Your videos really makes a sense if we leave those boring session on statistics. Now i feel really confident that I get my intellect back and able to do the real brainy stuffs as an engineer should do. Kindly suggest me in what way i could master over statistics & SS concepts. Thanks again, Regards, Pavan
Thanks jbstatistics, this actually cleared things up for me. I'm not used to this approach, I've only used the p-value method for hypothesis testing. Keep it up!
@jbstatistics
7 жыл бұрын
I have a strong preference for the p-value approach, but the rejection region approach has its place and it is a useful thing to know. Cheers.
Thanks!
Do we accept or reject the null hypothesis if the calculated value is *equal* to the critical value?
the fact that the test statistic will fall under a normal distribution (if the null hypothesis is true) is a consequense of the CLT?
Secondly why do you look at left tale if alternative less than null and right if alternative greater than null?? Please I am looking for the definitions for these or proof and I CANNOT FIND A THING.
why are we using -3, 0, 3 for the normal distribution graphs at the end? Will it always stay the same or do we change based in scenario?
thank you so much. Save me a lot of time reading the boring books.
@jbstatistics
10 жыл бұрын
You are very welcome.
Very helpful video
Why should you assume standard normal distribution if the μ0 is true?
Sir ,can u explain we have alpha value but not the confidence interval,like for .Z0.10=1.28 for one sided tail.How to solve from table if the critical value is not given in question. .
Omg! You are so awesome! Ty very much. :-)
you are a star .. thanks from deep heart :)
@jbstatistics
8 жыл бұрын
+Abdullah Adam You are very welcome!
@leepoking
7 жыл бұрын
really love you videos and thank you
@jbstatistics
7 жыл бұрын
You're very welcome!
really u r awsome...............so easy to understand.......i will recommend other to see this video
@jbstatistics
7 жыл бұрын
Thanks for the compliment!
Can someone explain me without using confidence intervals why we think that we we shouldn't reject Ho in the middle and reject it to the tails? Please give me mathematics definitions if possible So why do we look at ABS(Z) >=ABS(za|2) and not
great videos
True helper
"Panagiotis Goulas 4 years ago Secondly why do you look at left tale if alternative less than null and right if alternative greater than null?? Please I am looking for the definitions for these or proof and I CANNOT FIND A THING."
@jbstatistics
6 жыл бұрын
The test statistic is (X bar - mu_0)/(sigma/sqrt(n)). What values of the test statistic lead to evidence that the true mean is less than mu_0? Well, when the true mean is less than mu_0, X bar will tend to be less than mu_0, and the test statistic will be negative. Values in the far left tail of the distribution happen when X bar is much less than mu_0, and this gives evidence that the true mean is less than the hypothesized mean. Substitute "greater than" for "less than" for the right tailed argument.
@davidgheghia5408
6 жыл бұрын
Thank you.
You keep saying that we are finding the Z value with the use of software. Can you make a video possibly showing where you arrived at that or what software specifically you used?
@hussamm9605
6 жыл бұрын
He's using RStudio:)
thanks alot
What part of Canada are you from? You could totally make a lot of money off this, I'm at McMaster University taking nuclear engineering and you teach statistics in videos better than any of the profs here could ever teach it in person. Thanks for all the help, it's greatly appreciated.
Why do you sometimes divide alpha/2 and other times you dont?
@maggierobertson5741
7 жыл бұрын
I think it depends on what the question is asking. If it says u does not equal u0, then it's two sided. If it says that u is greater than u0, you would have only one sided.
thanks
Da real mvp.
For t test is the rejection process different ?
@jbstatistics
3 жыл бұрын
The process and logic are the same, but the critical value would be found from the t distribution with the appropriate degrees of freedom rather than the standard normal distribution.
thaaaaaaaaaaaaaank you... how do v repay u.....
Thanks! And you're welcome!
shouldn't we find the Z value for alpha/2 in the first example? the given alpha was equal to = 0.1, shouldn't we find the Z value that gives us an area of 0.05 to the right? (z=1.65) I'm confused
@jbstatistics
5 жыл бұрын
The first example is a one-sided test (the alternative is mu > mu_0), so we put the entire alpha level in the upper tail.
@12343469
5 жыл бұрын
@@jbstatistics Thank you for your quick reply
Hi Sir, may be it's my english problem, but what do you mean when you repeatedly said "if this null hypothesis is true, then the test statistics (Z) will have a standard normal distribution" ? To me, that statement means the (X bar - population mean) distribution will not be normal if the null hypothesis is wrong, but how does a wrong population mean change the shape of the distribution ?
@jbstatistics
Жыл бұрын
"will not be normal" It's not that it won't be normal, it's that it won't be *standard* normal. You are correct in that changes in the population mean won't change the shape of the distribution of that test statistic, but it will shift its distribution to the left or right. If the population mean does not equal the hypothesized mean, then the mean of that test statistic's distribution will not be 0, and thus the test stat won't have the standard normal distribution.
@weisanpang7173
Жыл бұрын
@@jbstatistics Thank you sir, that cleared my confusion. Your selfless sharing of your knowledge and making sure that people can actually understand can really change people's lives for the better.
you are amazing
@jbstatistics
7 жыл бұрын
Thanks!
How do you come up with 1.96?
@jbstatistics
7 жыл бұрын
As I describe in the video, it's the value of a standard normal random variable that yields an area to the right of 0.025, and it can be found using software or a standard normal table.
for Z score of 0.99, isn't it equal to 2.58, not 2.33?
@jbstatistics
5 жыл бұрын
No, the value I give in the video is correct. That example involves a one-sided alternative (a left-tailed test), and so the entire alpha value is put in the left tail. The z value that yields an area to the left of 0.01 is -2.33, to two decimal places. Had it been a two-sided alternative, with alpha = 0.01, then the critical values would be -2.58 and 2.58.
@ateasech
5 жыл бұрын
@@jbstatistics i am a newbie in statistic, would you please explain how to arrive at the values of 2.58 or 2.33. Any link or material would be of great help. thanks in advance
@ateasech
5 жыл бұрын
watched it a second time & got my answer. Your explanations are awesome and helped me to solve the Null hypothesis problems easily. Greetings from India
The probability of me giving you a like is about 110%.
@jbstatistics
6 жыл бұрын
Thanks :)
o sir ji love you
I have no clue what he’s saying.
Those vidoes really loose value if you compute statistics without providing first the formula one uses. Some parts here are confusing, and when you provide numbers it looses the value. People need to understand which formula one uses and why, computing anything is not a issue anymore these days.
@jbstatistics
Жыл бұрын
These videos would lose value if every time I used a value from the standard normal distribution, I had to explain where that value came from and what the standard normal distribution is. I would be backtracking, repeatedly, in all sorts of videos, thereby wasting the time of students who are up to speed and losing the point of the current discussion. This video comes at a point where students should be very familiar with the standard normal distribution. If they are not, then they should not be watching this video as they do not have the required background knowledge. There's a reason why we discuss the standard normal distribution, and how to get values from it, comes long before we discuss z tests. I discuss the standard normal distribution, and how to find areas and percentiles from it, in detailed fashion in other videos. There are various table formats, software functions, web apps, etc., so there are many different ways of getting these values.