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.

[@charlesomwoyo5904]

This one of the most direct and clear video I have ever seen. Straight to the point, thanks man!

[@Shumayal]

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]

Should be the null hypothesis.

[@jbstatistics]

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!

[@chaitanyaupadrasta7846]

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

[@mohammadrezanargesi2439]

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[@itsevennow]

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[@jbstatistics]

Thanks so much!!! I'm very glad you've found my videos helpful. All the best!

[@ayanamiareyes6481]

I literally love you so much. So much simpler than it seems in my notes.

[@a.yigitapaydn3333]

You are an hero. Your teaching is the best.

[@extrememike]

Best explanation of "rejection region" in youtube

[@बिहारीभायजी]

I studied from almost 15 videos at youtube, This is the beat content.

[@xinchen1392]

Man, your 10-minute-video explains what my professor could not explain in two months..

[@mahbubhasan8194]

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[@marykassouf8967]

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[@m_riatik]

im already crying

[@jbstatistics]

You're welcome! Best of luck on your test.

[@jbstatistics]

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.

[@egotisto]

cramming rn and this is ultra helpful! thanks dude :)

[@jbstatistics]

Thanks Vinayak! I'm glad you find my videos helpful.

[@valeriereid2337]

Thank you, Professor.

[@jbstatistics]

You are very welcome!

[@hussaanalvi9851]

You are excellent.Great explanation by a great teacher,thanks a lot :)

[@jbstatistics]

You are very welcome, and thanks for the compliment!

[@ebutuoydapi8709]

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[@hainguyenau]

thank you so much. Save me a lot of time reading the boring books.

[@jbstatistics]

You are very welcome.

[@Citidel36]

Your videos are awesome. You have enough material that you should consider a full Coursera or edX offering.

[@Am00973]

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[@jbstatistics]

Thanks!

[@linneajohansson3796]

This is truly brilliant! Thanks a lot!!

[@atefsiddiqui6085]

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]

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.

[@mohammedyalferjany9331]

you are a star .. thanks from deep heart :)

[@jbstatistics]

+Abdullah Adam You are very welcome!

[@leepoking]

really love you videos and thank you

[@jbstatistics]

You're very welcome!

[@pavanu8491]

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

[@atanusamanta8162]

really u r awsome...............so easy to understand.......i will recommend other to see this video

[@jbstatistics]

Thanks for the compliment!

[@NutPae]

your videos are just amazing! thank you!

[@jbstatistics]

Thanks!

[@provadas3507]

Very helpful video

[@thecowthatgoesmoo]

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.

[@cheesiechess3656]

what if I have a so called nested hypothesis so that my H0: is my

[@jyotimala8830]

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. .

[@marlaf2712]

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?

[@jbstatistics]

Thanks! And you're welcome!

[@weisanpang7173]

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]

"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]

@@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.

[@iKimJK]

True helper

[@davidgheghia5408]

"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]

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]

Thank you.

[@zulkh4iri314]

thanks alot

[@GNUopen]

great videos

[@hemangahuja9029]

thanks

[@brianvasquez6834]

Omg! You are so awesome! Ty very much. :-)

[@tapaseedeb104]

Do we accept or reject the null hypothesis if the calculated value is *equal* to the critical value?

[@panagiotisgoulas8539]

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

[@panagiotisgoulas8539]

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.

[@krystalkwan2363]

Why should you assume standard normal distribution if the μ0 is true?

[@MichalisFloyd]

the fact that the test statistic will fall under a normal distribution (if the null hypothesis is true) is a consequense of the CLT?

[@jsx0328]

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?

[@hussamm24]

He's using RStudio:)

[@aussie3851]

The probability of me giving you a like is about 110%.

[@jbstatistics]

Thanks :)

[@12343469]

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]

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]

@@jbstatistics Thank you for your quick reply

[@richardl.4374]

For t test is the rejection process different ?

[@jbstatistics]

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.

[@user-sp6os6tc2r]

Da real mvp.

[@12310936]

you are amazing

[@jbstatistics]

Thanks!

[@SnowP1997]

Why do you sometimes divide alpha/2 and other times you dont?

[@maggierobertson5741]

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.

[@JAWS99]

I have no clue what he’s saying.

[@SnowP1997]

How do you come up with 1.96?

[@jbstatistics]

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.

[@ibatubara]

for Z score of 0.99, isn't it equal to 2.58, not 2.33?

[@jbstatistics]

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]

@@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]

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

[@AbdullahPunctureWale-BePgCxx]

thaaaaaaaaaaaaaank you... how do v repay u.....

[@WojciechowskaAnna]

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]

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.

[@manjeetsingh-rc3gb]

o sir ji love you