It's because the values in the table tell you the probability that something is less than or equal to that value. So if you are wanting something that is greater than or equal to, you subtract the probability from 1, but then it means you've jumped up one. For example, let's say from the table that P(X=10)=0.3. If 0.7 is covering 1,2,3,4,5,6,7,8,9, then 0.3 (which is the remaining probability) must therefore be 10,11,12,13,14,...etc. Hence we can just bump one onto the value in the table to flip the probability from the one in the table to 1-the one in the table. Hope that helps!
Hi sir , at 12:18 you mentioned that the actual sig level is [1-0.9568 ] .Why did we use that instead of the probability of the critical value, in this case 0.9806 since cv=13
Because 0.9806 represents the probability of it being 13 or less. 1 - this means the remaining section, which is actually 14 or more. We want the critical region as 13 or more, so actually look at the value associated with 12 or lower, as the remaining part would be 13 or higher! Hope that helps!
hi sir, just wondering when identifying the critical region, do we need to show that the adjacent value does not fall into the critical region like it does in the book? thanks for the great video!
Hmmm I don’t think you need to, but it wouldn’t hurt. Check some mark schemes (loads of exam questions in my Google drive linked on my about page) and see what it looks like there?
Because we're actually calculating the probability that it is in the critical region, and that's not the value in the table, as that is the probability it is less than that value, not greater than!
Hi Sir, dont really understand this question from Mock Set 1 Paper 2:Q11B) hence find the x corodinate of the max turning point on curve with the equation y=f(3x)+5 etc the mark scheme is a bit confusing! Thank you :)
So start off by finding the x-coordinate of the maximum point Q for f(x) - this will not be the first solution you find, but the second one which is found by doing 2pi minus the one on the calculator. Now you can ‘transform’ this coordinate for f(3x) + 5. The +5 will do nothing to the x-coordinate, so all you need to do is divide you previous answer by 3 because it is compressed by a factor of a 1/3. The next part of the question is really sneaky - because of the minus f(1/4 x), it has flipped vertically, so the maximum from f(x) is now the minimum! As they want the maximum, you have to find the minimum of f(x), and then multiply it by 4 to account for the stretch of factor 4 represented by the 1/4 x. I hope that helps!
So consider the range of cos - it’s between 1 and -1. Now if it’s been squared, the biggest you can get is 1, and the smallest is now 0 (which comes from 0 squared). The function has been multiplied by 4, so the max is now 4, and the min is still 0. Hence the range is 0 to 4. 👍🏼
12:09 , shouldn't it be x>13 and not greater *and* equal to 13. P(x>=13) gives me 1-0.9658 = 0.0432 and hence its bigger than the required 0.025, so 13 would not be in the critical region however you included it in the critical region ? Love your Channel 👌🏾
It would be as you say if it were 2.5%, but it is a 5% sig level (and I don't think that it is two tailed, in which case it would be 2.5%!). Thank you! :)
They might give you the probability for an observed statistic. This is the p value. If the p value is less than the significance level then you reject H0. If it’s more, then accept H0. 👍🏼
When trying to find the critical region for the upper tail in a two tail test, we follow the principle of just finding the number closest to the significance level value rather than adding 1?
It will depend on the question whether it wants the probability to be less than the significance level, or to be closest to it - if it wants it to exceed it, then we use the +1 trick.
If the probability is below the significance level, then it appears NOT to be due by chance - if the probability is higher than the significance level, it seems likely it happened just by chance
Hi sir, in some past paper questions (old spec) they have the critical region as being the value closest to the significant level, even if doesn't fall below this. I assume this changed for the new spec and the critical region is only considered as the values where you reject the null hypothesis?
They will say in the question what they are looking for - the standard is to go below the sig level, but they MIGHT say something like find the value so that the probability is as close as possible to the sig level, in which case you'll follow that!
Hi Sir, I know this video is quite old but if you do see my comment can you explain why if the probability of something is less than the significance level that means you can reject the null hypothesis.
All the calculations we are doing are assuming that the null hypothesis is true, right? So if we calculate a probability for something happening given that setup, and it is incredibly unlikely (ie it is lower than the significance level) then this suggests that our assumption the null hypothesis is true may not have been so sensible. So we can therefore reject it! It doesn’t mean that it is definitely false, it’s just very unlikely that it is true. Hope that helps!
To find the 'other end' of the probability as the table shows less than or equal to a value, so subtracting from 1 finds greater than or equal to the value above it!
I’m currently updating this playlist to improve it - the ones without numbered titles in this playlist are a “complete” playlist, and videos 1, 2 and 3 are the ones I’m currently recording. I realise that’s a bit confusing! Sorry!
![A-Level Maths: O2-07 [Binomial Hypothesis Testing: Finding the Critical Region]](http://i.ytimg.com/vi/xwlkpT4LLmg/mqdefault.jpg)
so confusing aaaa
At 13:36 why do we have to increase the value of x by one and why does this apply only for the bottom of the table?
It's because the values in the table tell you the probability that something is less than or equal to that value. So if you are wanting something that is greater than or equal to, you subtract the probability from 1, but then it means you've jumped up one. For example, let's say from the table that P(X=10)=0.3. If 0.7 is covering 1,2,3,4,5,6,7,8,9, then 0.3 (which is the remaining probability) must therefore be 10,11,12,13,14,...etc. Hence we can just bump one onto the value in the table to flip the probability from the one in the table to 1-the one in the table. Hope that helps!
Hi sir , at 12:18 you mentioned that the actual sig level is [1-0.9568 ] .Why did we use that instead of the probability of the critical value, in this case 0.9806 since cv=13
Because 0.9806 represents the probability of it being 13 or less. 1 - this means the remaining section, which is actually 14 or more. We want the critical region as 13 or more, so actually look at the value associated with 12 or lower, as the remaining part would be 13 or higher! Hope that helps!
hi sir, just wondering when identifying the critical region, do we need to show that the adjacent value does not fall into the critical region like it does in the book? thanks for the great video!
Hmmm I don’t think you need to, but it wouldn’t hurt. Check some mark schemes (loads of exam questions in my Google drive linked on my about page) and see what it looks like there?
@@BicenMaths thank you! i'll do that and let you know
it's been two years, you didn't let him know yet😢
@@yahiaaa3 LMAOOOOO😭😭
8:52 why inside the mini brackets Is the b-1, I understand why u made it 1-p()but why was subtracting 1 from b asweell necesary
The value B is included in the bit you want to keep, so you subtract one from it as you need to take that probability away from 1
hi, at 11:15 why do you subtract the actual significance level away from 1 but in the previous example 6:48 you kept the actual significance level?
Because we're actually calculating the probability that it is in the critical region, and that's not the value in the table, as that is the probability it is less than that value, not greater than!
Hi Sir, dont really understand this question from Mock Set 1 Paper 2:Q11B) hence find the x corodinate of the max turning point on curve with the equation y=f(3x)+5 etc the mark scheme is a bit confusing! Thank you :)
So start off by finding the x-coordinate of the maximum point Q for f(x) - this will not be the first solution you find, but the second one which is found by doing 2pi minus the one on the calculator. Now you can ‘transform’ this coordinate for f(3x) + 5. The +5 will do nothing to the x-coordinate, so all you need to do is divide you previous answer by 3 because it is compressed by a factor of a 1/3. The next part of the question is really sneaky - because of the minus f(1/4 x), it has flipped vertically, so the maximum from f(x) is now the minimum! As they want the maximum, you have to find the minimum of f(x), and then multiply it by 4 to account for the stretch of factor 4 represented by the 1/4 x. I hope that helps!
@@BicenMaths oh that was sneaky! Thank you 😃- one last question how would you find the range of f(x)= 4cos^2(3x)
So consider the range of cos - it’s between 1 and -1. Now if it’s been squared, the biggest you can get is 1, and the smallest is now 0 (which comes from 0 squared). The function has been multiplied by 4, so the max is now 4, and the min is still 0. Hence the range is 0 to 4. 👍🏼
@@BicenMaths thank you so much:)
because it was only uploaded yesterday i dont know if there's more content
There is more
12:09 , shouldn't it be x>13 and not greater *and* equal to 13.
P(x>=13) gives me 1-0.9658 = 0.0432 and hence its bigger than the required 0.025, so 13 would not be in the critical region however you included it in the critical region ?
Love your Channel 👌🏾
It would be as you say if it were 2.5%, but it is a 5% sig level (and I don't think that it is two tailed, in which case it would be 2.5%!). Thank you! :)
Hi Sir, i also wanted to ask how do you do a p value test for normal distribution. thank you :)
They might give you the probability for an observed statistic. This is the p value. If the p value is less than the significance level then you reject H0. If it’s more, then accept H0. 👍🏼
such a great simple answer thank you!
When trying to find the critical region for the upper tail in a two tail test, we follow the principle of just finding the number closest to the significance level value rather than adding 1?
It will depend on the question whether it wants the probability to be less than the significance level, or to be closest to it - if it wants it to exceed it, then we use the +1 trick.
wait so when a number if below the significance level e.g 5 then that means it is due by chance?
If the probability is below the significance level, then it appears NOT to be due by chance - if the probability is higher than the significance level, it seems likely it happened just by chance
@@BicenMaths yup understand now cheers
sir shouldn't it be p=0.05 and not p=0.5 at 14:00
Hmm we are saying that the probability of the coin is 0.5, but the significance level is 0.05
Hi sir, in some past paper questions (old spec) they have the critical region as being the value closest to the significant level, even if doesn't fall below this. I assume this changed for the new spec and the critical region is only considered as the values where you reject the null hypothesis?
They will say in the question what they are looking for - the standard is to go below the sig level, but they MIGHT say something like find the value so that the probability is as close as possible to the sig level, in which case you'll follow that!
how do i know when to use binomial PD or binomial CD 😭
PD is for X=a, CD is for X
@@BicenMaths lifesaver thank youu 🙏
Hi Sir, I know this video is quite old but if you do see my comment can you explain why if the probability of something is less than the significance level that means you can reject the null hypothesis.
All the calculations we are doing are assuming that the null hypothesis is true, right? So if we calculate a probability for something happening given that setup, and it is incredibly unlikely (ie it is lower than the significance level) then this suggests that our assumption the null hypothesis is true may not have been so sensible. So we can therefore reject it! It doesn’t mean that it is definitely false, it’s just very unlikely that it is true. Hope that helps!
Sir In the textbook they don’t add one to the p>???
This technique is just a shortcut, so it probably wouldn't be in any textbook.
Sir please why did you subtract the 0.9568 from 1
To find the 'other end' of the probability as the table shows less than or equal to a value, so subtracting from 1 finds greater than or equal to the value above it!
do they still give the tables
Yes, they are in the formula booklet towards the end.
9:26
is this all the videos for this topic?
I’m currently updating this playlist to improve it - the ones without numbered titles in this playlist are a “complete” playlist, and videos 1, 2 and 3 are the ones I’m currently recording. I realise that’s a bit confusing! Sorry!
@@BicenMaths sir is the table cumulative probability?
Yes it is!
@@BicenMaths thank you!
Sir, could pls explain when to exactly minus the probability u get by 1 . i don't get that bit
Pls explain.
If you were asked to find the probability X >= 13 for a binomial distribution, you would find 1-P(X