This understands so much thank you so much and also i just play it at 1.75x speed as you talk a bit slow (not to be rude sorry) just wish to ace the test tomorrow for my mocks :)
If I just remember the definitions of critival value/critical region/significance level, can I get away with just doing the one tailed test without it as I still dont understand it as we werent taught this
so if the probability that we are assuming to be true ends up being lower than the significance level, we always reject it. and if it ends up being greater than the significance level, then we always say that there is insufficient evidence to reject the null hypothesis. is this always true?
That is correct! We are assuming that H0 is true when we make calculations, so if the probability we calculate is very small, this makes us think that H0 is unlikely to be true, so we reject it. If the probability is large, it means H0 is probably true, so we don't reject it!
@@BicenMathsthank you so much, i have been watching all of your videos on pure and applied and they’ve helped me improve so much. I have mocks in 2 weeks and I’m sure i’ll be able to get an A/A*, and the credit for that will go to you, thank you again so much and please continue to help others like myself.
Sir for the last question i did the critical region and got (x>=4) as H1: p > 0.4 so (100% - 5% is 95% so we choose the number above the one just getting more than 95% as a probability). 11 is greater than 4 so dont we reject H0 ??!?? I don't understand where i went wrong :(
The probability that X>=4 will be very high, as there are 20 trials with probability of 0.4. This means you'd expect 8 of them to be successful, so there's a very high chance there would be more than or equal to 4! I think perhaps you have found the other end of the critical region, which is that X0.4
Because the table tells you the probability of 6 or less. 6 or less has a probability of 0.9648, meaning 7 or more is 1-0.9648, which is less than 0.05. If you did 6 or more, it would be 1-0.8554 which is more than 0.05, so isn’t significant. The earlier videos in the playlist explain it I believe.
Not dumb at all. If the probability that it occurred with the given binomial distribution and given probability, then it’s saying there’s enough likelihood that this probability is true. If the probability of it occurring with the given probability was very low, then it’s likely this probability isn’t true, and in fact it’s what the alternative hypothesis is suggesting!
I do use it! I just don’t like using the inverse binomial for critical regions, I way prefer to use the tables if the probability is in the table - it’s just easier to see the critical region more visually. Trust me, it’s a much better way of quickly finding the values, rather than having to sensibly guess what value to input into the calculator. Try it with the tables!
I didn’t specialise in statistics - however, the significance level is always selected by the statistician/researcher, and will be chosen according to how “strong” they want their test to be, as well as things like the size of the sample taken. The actual significance level is the probability that you INCORRECTLY reject the null hypothesis (in other words your conclusion that the probability has changed is wrong!) - so if you have a lower significance level, and the null is rejected, this means the test and its conclusion are stronger/more powerful than a test with a high significance level. It’s interesting to consider that even when your observed data goes below that significance level, it doesn’t mean that the probability has definitely changed - just that it is very likely that it has!
Particle physics uses something called '5 sigma' which essentially means that they have to be 99.9999% certain before they claim a discovery. www.theguardian.com/science/life-and-physics/2014/sep/15/five-sigma-statistics-bayes-particle-physics
You are incredible
Bro is saving me rn
This understands so much thank you so much and also i just play it at 1.75x speed as you talk a bit slow (not to be rude sorry) just wish to ace the test tomorrow for my mocks :)
If I just remember the definitions of critival value/critical region/significance level, can I get away with just doing the one tailed test without it as I still dont understand it as we werent taught this
I’m sure that’d be fine, but if you watch my videos introducing hypothesis testing, I’d like to think you’ll be able to understand it better!
so if the probability that we are assuming to be true ends up being lower than the significance level, we always reject it. and if it ends up being greater than the significance level, then we always say that there is insufficient evidence to reject the null hypothesis. is this always true?
That is correct! We are assuming that H0 is true when we make calculations, so if the probability we calculate is very small, this makes us think that H0 is unlikely to be true, so we reject it. If the probability is large, it means H0 is probably true, so we don't reject it!
@@BicenMathsthank you so much, i have been watching all of your videos on pure and applied and they’ve helped me improve so much. I have mocks in 2 weeks and I’m sure i’ll be able to get an A/A*, and the credit for that will go to you, thank you again so much and please continue to help others like myself.
@@dayan5669 The credit will all be down to you - you are the one who is working hard and learning new things! Keep it up, let me know how it all goes!
@@BicenMathswill do, thank you again
could it be like this where you are assuming the h1 is true and that rule applies .. or am i over stressing this lol@@BicenMaths
could we use the critical region method for 8:00
Absolutely. Unless they tell you which method to use, you can choose to use either!
Sir for the last question i did the critical region and got (x>=4) as H1: p > 0.4 so (100% - 5% is 95% so we choose the number above the one just getting more than 95% as a probability). 11 is greater than 4 so dont we reject H0 ??!??
I don't understand where i went wrong :(
The probability that X>=4 will be very high, as there are 20 trials with probability of 0.4. This means you'd expect 8 of them to be successful, so there's a very high chance there would be more than or equal to 4! I think perhaps you have found the other end of the critical region, which is that X0.4
@@BicenMaths Op thats exactly where I went wrong, I found the wrong end. Thankyou sir :)
At 13:00, are we saying there is a 12.75% chance that there are more than 11 patients which are successfully treated?
Yes, given the assumption that p=0.4
at 6:13 , why do you not use the significant value as 0.95 putting it between 0.8554 and 0.9648? so the critical region would be X>=6?
Because the table tells you the probability of 6 or less. 6 or less has a probability of 0.9648, meaning 7 or more is 1-0.9648, which is less than 0.05. If you did 6 or more, it would be 1-0.8554 which is more than 0.05, so isn’t significant. The earlier videos in the playlist explain it I believe.
This might be the stupidest question ever, but at 1:17, how do you know the probability of getting heads is 0.5?
Equal chance of heads or tails on a coin! 50:50 or 0.5 👍🏼
Dumbass
At 1:25, where did you get the parameter 0.5 from?
oh nevermind i get it now
hey sir at 3:39, instead of saying "insufficient evidence to reject h0" is it valid to say "reject h1 and accept h0" instead?
Yes that would be fine!
@@BicenMaths thanks
This may be a dumb question but why is that if the prob is higher than sign. level there isn’t enough evidence
Not dumb at all. If the probability that it occurred with the given binomial distribution and given probability, then it’s saying there’s enough likelihood that this probability is true. If the probability of it occurring with the given probability was very low, then it’s likely this probability isn’t true, and in fact it’s what the alternative hypothesis is suggesting!
why dont you use the distributions mode on your graphics calculator ?
I do use it! I just don’t like using the inverse binomial for critical regions, I way prefer to use the tables if the probability is in the table - it’s just easier to see the critical region more visually. Trust me, it’s a much better way of quickly finding the values, rather than having to sensibly guess what value to input into the calculator. Try it with the tables!
In the real world, how is the significance level determined?
I didn’t specialise in statistics - however, the significance level is always selected by the statistician/researcher, and will be chosen according to how “strong” they want their test to be, as well as things like the size of the sample taken. The actual significance level is the probability that you INCORRECTLY reject the null hypothesis (in other words your conclusion that the probability has changed is wrong!) - so if you have a lower significance level, and the null is rejected, this means the test and its conclusion are stronger/more powerful than a test with a high significance level.
It’s interesting to consider that even when your observed data goes below that significance level, it doesn’t mean that the probability has definitely changed - just that it is very likely that it has!
Particle physics uses something called '5 sigma' which essentially means that they have to be 99.9999% certain before they claim a discovery. www.theguardian.com/science/life-and-physics/2014/sep/15/five-sigma-statistics-bayes-particle-physics
This is great, Andy, thanks for sharing!
Sir say for the last question we were testing for below so the number of successful treatments was lower would we do P(X/
Yes we would switch to less than or equal to!