Hi sir, I'm really confused about why you're not rejecting the null hypothesis when your value is greater than the sL. eg at 24:46 . Isn't that what you're supposed to do
We accept the null hypothesis if the probability is higher than the significance level - this is because it is likely enough to have happened with the null hypothesis being true!
@@BicenMaths for one/two-tailed normal distribution hypothesis q's with the sample mean, do we have to always make sure we take the P(sample mean less than or greater than a value of the mean given)? e.g, say the sample mean is y = 5.52 and the normal distribution is Y - N (5.7, 0,08^2/30), where HO: mean = 5.7, and H1: mean less than 5.7 with sig level of 2.5%? so in this example, would you take P(X bar as less than 5.52)?
@cineacle yes that’s right - if the mean you observed is smaller than the mean you are testing in H0, you test less than the observed value, and if it is bigger than the mean you are testing you test greater than the observed value.
For the second question at 21:12 of the video. Would I need to do 1- P(X bar ≤ 124) when using the other calculator . I got 0.04778 without doing 1- the probability . Can you explain this to me please ? Thank you
Hi Mr Bicen, at 20 minutes while doing the hypothesis tests, do you not need to do the continuity correction as it is a binomial approximation? So instead of P(X>124), P(X>124.5). Also I appreciate your videos, very helpful.
Just not really sure when and where we are supposed to use continuity corrections. Is it not used when hypothesis testing with binomial approximation as we are dealing with means? And otherwise if with normal data and approximating we should?
You would need to use a continuity correction when converting a binomial distribution to a normal one, but the here we're just testing a sample mean, which is already normally distributed (hence you're given the standard deviation and mean), so you'd just test the critical value they give you as is. hope this helps!
This is correct! We ONLY do continuity correction when using the normal distribution for a binomial distribution (i.e. we have just done the np, np(1-p) process) - never any other time.
I really struggle to understand the direction of the > or < in a two tailed test because I was taught for a one tail it always matches the alternative hypothesis its good if im unsure but it means idk how to figure to the direction of a two tail
Have a look at the observed value from the test statistic (in this case, it is the mean from the sample). If the mean from the sample is bigger than the H0 assumed mean, then you would investigate the probability that it is higher than the observed mean - and if the mean from the sample is lower, investigate the probability that it is lower than the observed mean. This is because these probabilities are naturally going to be smaller than the other way around.
Im struggling to understand for all types of hypothesis testing how you are supposed to know what the extreme probability would be for example how do you. Know you should find prob X 124
If your alternative hypothesis is that X > a, then when you find the test statistic, you'll find X >= the value observed. If it's X < b, then you'll find X
The 59.1 is the observation we made of the mean of the sample - so we want to test if this observation is ‘extreme’ to mean we reject H0. If you did it with
Hi Mr Bycen, I cant seem to get to the correct answer... any pointers? Machine makes metal sheets width X cm. Supervisor wants to use a sample to estimate the mean of X Determine how large the sample needs to be so that he can be 95% sure that the sample mean width will differ from the population mean width by less than 1 cm. Assume that sd=3.2cm. Any pointers highly appreciated.
This is a tough question that is too hard to explain on here! I think it's from the textbook though, have you used Solution Bank for it? Very unusual and not something I anticipate them asking.
@@BicenMaths hey thanks so much, yeh its long explenation so wasnt explecting one. Just wanted to see if you could think of a pitfall. I mean I used mu plus 1 on the Z formula..mu cancels..inv Normal 0.95 for Z value. Dont get the right answer and cant see where Im going wrong. Its from the official pearson workbook for year 2 Stats and Mech. I dont think they have a solution bank for that? Ive also booked my self for your session tmr. I think i wont be able to be there till the end so hopefully watch the last quarter when you send link to the whole thing, is that fairly quick? Thanks a lot for all your help.
@@AceOfHearts001 So, here's my advice - have a look at Q24 from Applied Year 2 textbook (not workbook) as it is asking a similar thing to do with how large the sample needs to be. Then you can review it using the Solution Bank and that should help you answer the one from the workbook! www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Factiveteach-prod.resource.pearson-intl.com%2Fr00%2Fr0071%2Fr007110%2Fr00711049%2Fcurrent%2Falevelsb_sm2_ex3mix.pdf As for Saturday's session, there's no problem if you need to leave earlier - I'll send out the recording as soon as it processed by Zoom and you can use it whenever convenient for you! See you Saturday!
Because the alternative hypothesis is that the mean is not the given value - meaning it could be higher or lower than this value. There are 2 options - higher, or lower. This makes it 2 tailed. If the alternative hypothesis was that it was higher than a given value, for example, it'd be 1 tailed.
Hi sir could we do the hypothesis testing via critical regions and inverse normal ? I've done it that way and come to the same conclusions as you do in the video.
your videos are amazing! I'm so glad I found your channel
Revision gang, where u at!
HAHAHAA LAST MIN REVISION GANG FR🤣🤣
Hi sir, I'm really confused about why you're not rejecting the null hypothesis when your value is greater than the sL. eg at 24:46 . Isn't that what you're supposed to do
We accept the null hypothesis if the probability is higher than the significance level - this is because it is likely enough to have happened with the null hypothesis being true!
hahaha the last example was funny
It’s a real job, all based on stats! 😂
@@BicenMaths for one/two-tailed normal distribution hypothesis q's with the sample mean, do we have to always make sure we take the P(sample mean less than or greater than a value of the mean given)?
e.g, say the sample mean is y = 5.52 and the normal distribution is Y - N (5.7, 0,08^2/30), where HO: mean = 5.7, and H1: mean less than 5.7 with sig level of 2.5%?
so in this example, would you take P(X bar as less than 5.52)?
@cineacle yes that’s right - if the mean you observed is smaller than the mean you are testing in H0, you test less than the observed value, and if it is bigger than the mean you are testing you test greater than the observed value.
@@BicenMathsthat makes sense, thank you sir!
For the second question at 21:12 of the video. Would I need to do 1- P(X bar ≤ 124) when using the other calculator . I got 0.04778 without doing 1- the probability . Can you explain this to me please ? Thank you
It’s the same value, just slightly rounded!
Hi Mr Bicen,
at 20 minutes while doing the hypothesis tests, do you not need to do the continuity correction as it is a binomial approximation? So instead of P(X>124), P(X>124.5).
Also I appreciate your videos, very helpful.
Just not really sure when and where we are supposed to use continuity corrections. Is it not used when hypothesis testing with binomial approximation as we are dealing with means?
And otherwise if with normal data and approximating we should?
@@benyeo9663me too I never know when to do the continuity correction
You would need to use a continuity correction when converting a binomial distribution to a normal one, but the here we're just testing a sample mean, which is already normally distributed (hence you're given the standard deviation and mean), so you'd just test the critical value they give you as is. hope this helps!
This is correct! We ONLY do continuity correction when using the normal distribution for a binomial distribution (i.e. we have just done the np, np(1-p) process) - never any other time.
@@BicenMaths Okay that makes more sense.
Thank you.
I really struggle to understand the direction of the > or < in a two tailed test because I was taught for a one tail it always matches the alternative hypothesis its good if im unsure but it means idk how to figure to the direction of a two tail
Have a look at the observed value from the test statistic (in this case, it is the mean from the sample). If the mean from the sample is bigger than the H0 assumed mean, then you would investigate the probability that it is higher than the observed mean - and if the mean from the sample is lower, investigate the probability that it is lower than the observed mean. This is because these probabilities are naturally going to be smaller than the other way around.
@@BicenMaths tysm sir really appreciate you and your vids
Thank you!
You’re welcome! :)
Im struggling to understand for all types of hypothesis testing how you are supposed to know what the extreme probability would be for example how do you. Know you should find prob X 124
If your alternative hypothesis is that X > a, then when you find the test statistic, you'll find X >= the value observed. If it's X < b, then you'll find X
Why did you do y
The 59.1 is the observation we made of the mean of the sample - so we want to test if this observation is ‘extreme’ to mean we reject H0. If you did it with
Hi Mr Bycen, I cant seem to get to the correct answer... any pointers?
Machine makes metal sheets width X cm. Supervisor wants to use a sample to estimate the mean of X
Determine how large the sample needs to be so that he can be 95% sure that the sample mean width will differ from the population mean width by less than 1 cm. Assume that sd=3.2cm.
Any pointers highly appreciated.
This is a tough question that is too hard to explain on here! I think it's from the textbook though, have you used Solution Bank for it? Very unusual and not something I anticipate them asking.
@@BicenMaths hey thanks so much, yeh its long explenation so wasnt explecting one. Just wanted to see if you could think of a pitfall. I mean I used mu plus 1 on the Z formula..mu cancels..inv Normal 0.95 for Z value.
Dont get the right answer and cant see where Im going wrong.
Its from the official pearson workbook for year 2 Stats and Mech. I dont think they have a solution bank for that?
Ive also booked my self for your session tmr. I think i wont be able to be there till the end so hopefully watch the last quarter when you send link to the whole thing, is that fairly quick?
Thanks a lot for all your help.
@@AceOfHearts001 So, here's my advice - have a look at Q24 from Applied Year 2 textbook (not workbook) as it is asking a similar thing to do with how large the sample needs to be. Then you can review it using the Solution Bank and that should help you answer the one from the workbook! www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Factiveteach-prod.resource.pearson-intl.com%2Fr00%2Fr0071%2Fr007110%2Fr00711049%2Fcurrent%2Falevelsb_sm2_ex3mix.pdf
As for Saturday's session, there's no problem if you need to leave earlier - I'll send out the recording as soon as it processed by Zoom and you can use it whenever convenient for you! See you Saturday!
@@BicenMaths Thats a really good suggestion! I will do just that.Thank you. Looking forward to tmrs session!.
@@AceOfHearts001 Great! Just in case you haven't realised, the session is on Saturday morning, not tomorrow! Hope you can still make it?
Thanks sir
No problem 👍🏼
How do you know it is a 2 tailed test
Because the alternative hypothesis is that the mean is not the given value - meaning it could be higher or lower than this value. There are 2 options - higher, or lower. This makes it 2 tailed. If the alternative hypothesis was that it was higher than a given value, for example, it'd be 1 tailed.
Hi sir could we do the hypothesis testing via critical regions and inverse normal ? I've done it that way and come to the same conclusions as you do in the video.
Absolutely! Unless it states which way to do it, you can choose whichever method you prefer.