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Hyp testing #2: Testing for μ when σ is known.
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- Опубліковано 18 сер 2024
- Justin introduces two examples in order to explain the concept of conducting a formal hypothesis testing for μ when σ is known. The questions are provided below with time references.
One-tailed example (0:26):
The manager of a department store is thinking about establishing a new billing system for the store’s credit customers. She determines that the new system will be cost effective only if the mean monthly account is greater than $70. A random sample of 200 monthly accounts is drawn for which the sample mean account is $74. The manager knows that the accounts are normally distributed with a standard deviation of $30. Is there enough evidence at the 5% level of significance to conclude that the new system will be cost effective?
1.State Null and Alternate Hypotheses (1:40)
2.Calculate test statistic (4:13)
3.Consider decision rule (5:12)
3a. Calculate p-value (6:55)
4. State rejection decision (8:23)
5. Conclusion (9:28)
Two tailed example (9:58):
A new toll road is being built and financed on the expectation that 8,500 cars will use it per day. In the first 30 days of its operation, a daily average of 8,120 cars were found to have used the toll road. Using the 1% level of significance, test whether the expectation was incorrect. (Assume that the distribution of daily road users is normally distributed with a standard devation of 950)
1.State Null and Alternate Hypotheses (11:06)
2.Calculate test statistic (11:46)
3.Consider decision rule (11:58)
3a. Calculate p-value (13:28)
4. State rejection decision (14:21)
5. Conclusion (14:40)
You have summarised my 50 slides lecture presentation into 16 mins. You're the reason why I'll pass my data modelling unit. I want to support your channel, please tell me how. Thank you!
🌚🌚🙂
@@himanshu.j you are member of ‘men of culture’
Sir, I’m literally transcribing the different ways by which you phrase a point that you’re trying to explain.
I do so because that’s exactly what I wish more teachers would do.
Your multiple phrasing of one point, actually helps clear the air, and steers me in the right direction to how I’m supposed to view the problem and to mindset I should be in while trying to solve it at each step
It helped me gain the perspective you’re trying to give
Seriously, your continual re-phrasing of key points at each step REALLY HELPS a ton
THANK YOU
You need to create a patreon or something. Your videos alone will be the reason I'm able to finish my masters.
yeah there needs to be some kind of Patreon, I for one will be more than happy to support you Justin!
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I never would have thought that I'd be enjoying statistic videos and binge-watch them.. you have an amazing way of explaining these concepts and I admire your work :)
haha ikr
Great explanations! I took Prob & Stat class last year and ever since then I am more and more interested in statistics. Please keep creating new content. Your explanations are truly awesome!
You are a genius buddy, seriously this concept was flying over my head during lectures. My teacher could not teach this to me in 22 sessions, which you did in such a short time.
Your way of teaching is gr8...Yu cleared my every doubt in hypothesis testing...
Thankyou
Talented teacher!
Thank you for your contribution to society.
A short hand:
"If p is low, null must go! (reject)
If p is high, null must fly!" (fail-to-reject)
A short phrase will never confuse you again! (from jose - udemy)
Insanely good content. Best stats channel on the UA-cam
You are saving my life with these lessons. I love you
Thank you for the effort you put in your videos! They are very well organized, and you explain well!
I finally got a sense what hypothesis testing is ...thanks
Your videos really save me from my upcoming test next month
Isn't z critical is 1.96 when our level of confidence is 95%??
Yes but I think this is not two tailed test...instead is a left tailed test..hence the value of 1.645
Thank you for this fantastic video. And I really appreciate that you have added the questions in the description. I used python to solve them and copied the questions directly.
Thank you Justin for your awesome explanation!
I really really appreciate these videos big time! Do or did you work with R and would you plan on doing videos on R Studio, or not your domain?
no words for "Thank you "
im lost when u explain it using excel... where you get the 2.576? i can followed till u found the z=-2,191 after that i dont know :_)
I was hoping someone would explain this part more Too! 😅
Thank you...fantastic way of teaching...lot of depth understanding
Your videos are helping me SOOO much!!
jesus christ you are better than the godlike chemical tutor
you are highly appreciated,,,,,your teaching method is quite good and clear concept....now im gonna see your all videos😍😍😍😍
I'm lost at 13:29 . Where is the purple color -2.191 from? Is it related to the P-value?
It's coming from the formula, u'-u / (sigma/sqrt(n)) here u' = 8120, u = 8500, sigma = 950 and n = 30(since the average is taken over 30 days.)
@@akshatb hi ! should't the formula for p be something like 1-NORM.S.INV ? Very confused
Hi @zedstatistics, why didn't you use degrees of freedom = 29 for the second example to calculate the Z-Crit score? Thanks for your help ^^
Love your all videos... very well articulated.
Wow you make everything simple for me i really appreciate your work, well explained & well understood😍😍😍😍😍 i really love this ..
At 11:15 , if the problem was written as "test whether the expectation was CORRECT"
Then would the H1: meu = 8500 ?
As a general rule, you set the question that is being asked in the problem as H1, and its negation as H0
Please explain me how to calculate the p value. I am unable to understand.
thanks Justin. the question i have is: in what situation would you know the population standard deviation, but not be confident of the population mean? it sounds like a rare situation
so we basically pretend that hypothesised mean is the true population mean and then compare it to the sample mean to see how big is the difference, right?
but what about the true population mean? seems like we conveniently forgot about it
I don't understand why everything is the opposite regarding the null-hypothesis and the critical area... this makes it extremely difficult to comprehend, at least for me
The way I see it is that we're trying to find out whether (given the circumstances)
H0) The mean is above 70, so the change is beneficial for the company
H1) The mean is below or equal to 70, so the change is not beneficial
That means there'll be a left-side tail with the size of 5%: Why is the size of acceptance on the right side for you, and only the 5% area?
There is a murder in your town and you are on trial.
The prosecution is keen to infer your guilt.
Thankfully the null hypothesis is that you are innocent and the weight of evidence is for them to shift. But if they DO shift it, then this is a powerful statement of your guilt.
This is the way we treat WHATEVER hypothesis we are seeking to infer (ie. Say that the mean is above 70).
We start with the opposite stance and see if we can REJECT IT. Note that if we can reject this, it becomes a powerful statement in favour of the mean being greater than 70.
If we were to instead START with the null being mu > 70, then the best we can do is FAIL TO REJECT IT. This is a much less powerful statement.
Going back to the courtroom example, imagine that instead of the presumption of innocence, we started with the presumption of guilt and you had to PROVE your innocence. Can you really PROVE your innocence? Most likely many people would be "found" guilty under this premise because really "NOT ENOUGH EVIDENCE TO REJECT GUILT" it is a much weaker statement in favour of guilt than "ENOUGH EVIDENCE TO REJECT INNOCENCE".
@@zedstatistics effortlessly educating . Thanks
The fact that the accounts are normally distributed does not add any value here, right? Because, we are using central limit theorem to conclude that the sampling distribution is normal with a standard deviation equal to sigma/root(n), instead of using just sigma. So the accounts could be distributed in any way really, and this solution would still apply?
Finish the sentence at the end; once you make the conclusion of whether to reject or accept the null hypothesis, what does that mean in terms of the original question- using normal language instead of the double speak of hypothesis testing.
No matter how many videos I watch or books I read, everyone uses the same format to teach this subject: introduce the problem, explain the math, work the math, describe the answer in terms of the math, but then fails to translate that answer back into what the original problem is.
Example: in your second example problem, I do not know if the answer derived by the math means the toll road planners estimated traffic correctly or not.
I can't find the link for the calculation of P value neither for the average
how did he get 1.886 value to use in p value formula ?
I doubt my question will be answered, but: In the example with the department store credit accounts, why is a sample of 200 accounts used in the first place? Presumably the dept store has access to 100% of the knowledge about accounts, and can easily calculate the population mean and std dev in a few queries of their account management database. There's no point to the "sampling" part. I can see why the dept store managers would want to know if the population mean was "significantly greater than $70", but I don't think I've seen any examples for this specific case (either on this excellent youtube channel, or in my college stats textbook).
I ask because I work in a small manufacturing plant. We "grade" each and every item we produce and keep those results in a database. I was recently talking to my manager about if we use a rigorous statistical/numerical basis for decision making when trying a new technique in the manufacturing process--for example, if we have X failures with process A and X-delta failures with process B, is process B "significantly better" than process A. We have access to 100% of our data. So what's the "sample" when we can easily examine all the data? What test(s) do we use? All the normal tests are for samples drawn from some unobtainable population.
I didn't understood, how we considered that second example was of two tail test?
You’re fantastic
Sir,
when ever we reject the null hypothesis... we are face with two situations
1) The null hypothesis been false ... true positive
or
2)The null hypothesis been True ....false positive
Is this the reason why we can never conclude by saying the null hypothesis is true?
12:10
How do we know
That we should split the 1%in two tails?
I have a question! In the example of toll road, the standard deviation is of the sample or the population! I assume its the sample because the population parameters are unknown! Just wanted to confirm!
it's the standard deviation of the population, and yes it's not very realistic as he said, as you usually don't have any parameter about the population
what will be H1? if the question asks ....if the mean monthly account is not greater than $70.....
thanks so much! so useful for me !
13:33 Should 't the formula of p be 1-NORM.S.INV ? I thought I was understanding the topic lol
I didnt understand how did you get the critical value 1.645
Great video! Just one question, I though the calculation for z-value was z = (x - μ) / σ, why did you include √n? Dosen't that make the calculation for standard error? Regards, Johanna
You use this formula if you calculate the z-value for a certain value, not for a greater sample size. So n=1 and sqrt(1) is 1, so you can remove this from the formula shown in the video.
@ =(70-74)/(30/SQRT(200)) = -1.886. hi, why he didnt calculate Z-score as the formula above? Z-score of 70 is for sure negative because lower than mean of 74. If Z-score is -1.886, does it mean its less than 1.645 and pass?
One of the few people that you will want to see end up in paradise
thank you so much!
7:50
Sir is that the significance value of 3%?
Norm.s.dist=0.0142?? can you explain more
Man I really wish you would have gone the further step and not used the excel. Other than that it was an informative video, I had to go to other video's for further explanation without an excel.
he did say 1-the ztable value gives the pvalue
13:30 Did anyone notice him saying 567 instead of 576.
salute to your attention!
Where's the fucking link that you talked about in the video?
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You can never test anything like this. The t test has never,and will never,test anything. Application of statistical hypothesis testing as if it could actually test anything is incorrect always.
A strong early nomination for the 2021 Cynicism Awards
@@zedstatistics do you not agree that it's important to point out these things when science is suffering from people assuming you can test things with statistical hypothesis tests?