A-Level Maths: O2-07 [Binomial Hypothesis Testing: Finding the Critical Region]

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[@lilly8823]

Thank you. This was so helpful. When people ask me who my maths teacher is, I say your name instead of my actual teacher.

[@aceplayys7847]

+1

[@jacoballton4511]

+1

[@jonty4332]

=2

[@muhammadqureshi5271]

Quick maths

[@user-jt5cv5hg3n]

@M43K +1

[@Zextortgaming]

actually the GOAT I understood it so quickly Edit: I got an A on my test thanks very much

[@tris8703]

Spent weeks trying to figure this out on my own and here I am a day before my exam watching this and I finally understand it thank you so much

[@TLMaths]

Which exam do you have tomorrow? Best of luck!

[@willz4938]

Finally understood it a week and a bit from my UCAS prediction exams - the nation's favourite maths teacher!

[@k1ng724]

This man has carried me through Alevel Maths

[@hoyama1520]

I spent 7 hours trying to understand this and you just explained it in just 19 minutes, thanks for explaining it!!!!!!!!!!

[@TLMaths]

Glad it helped!

[@mtg2827]

I've been confused on this for ages, thanks for explaining it so clearly!!!

[@TLMaths]

Glad I could help!

[@a.k.2860]

Absolute saviour- got a maths STATS test in literally 20 minutes 👌🏻😭😰

[@puddleduck1405]

lol mines in an hour

[@efdbjon2114]

haha im oing my a level exam in half an hopur

[@DanielBateren]

mines in 4 hours

[@Chiefdark]

@@efdbjon2114 mines in 2h

[@iknowimwrongbut4491]

⁠@@efdbjon2114me with my a level today

[@leniw8121]

struggled with hypothesis regions - particularly critical regions for so long - so grateful for this video it finally makes sense :)

[@ahmedjamil8525]

Amazing...I am going to teach my student this testing first time in my life so after watching your awesome video my own concepts are crystal clear now. Thanks a lot Sir!

[@itachi6336]

6:30 the bit I didn't understand in my lesson. But I understand it now thanks to you

[@Milo-oe7cc]

such a good teacher especially for home learning. thanks teach!

[@fergusonmobile1812]

Absolutely fantastic. You are the best teacher I have ever seen

[@TLMaths]

Wow! High praise thanks!

[@mutsa9334]

thank you so much! was really struggling to get my head round this but you've saved me; please keep the videos coming :)

[@ray620]

Thank you - best teacher everrr

[@raiturner2132]

Extremely helpful. Thx so much!

[@alexewing2685]

Thank You so much for saving my mock. Been confused with this for well over a year now and finally understand it

[@brokke8388]

thank you so much for this, it finally makes sense!! you have an amazing way of explaining why we do everything

[@TLMaths]

Really glad I could help!!

[@binulamadhavan2802]

Thank you so much, sir. I didn't understand this earlier and now I understand it very well.

[@aryanameer8368]

omg you're the best. Thank you!

[@apatchy0664]

Wow. Literally the best video

[@cre556]

God bless you Teacher, many thanks for explaining this confusing topic and making it crystal clear ✨

[@s.a7711]

I actually understood what the critical region was and how to find it in one vid than what I learnt in year 12 for stats

[@dee.2848]

Can you use either technique (finding critical value vs looking at expected value) to conduct a Hypothesis Test? Or must you be able to do both? Thanks.

[@crackedizzy]

This actually helped so much, I've been struggling with it since first year and now I finally understand, tysm

[@emmanuelassor654]

thank you this was very clear and helpful, teacher at school was overcomplicating everything

[@skittlesboy8033]

Absolute legend

[@SIRMAPANDAONLINE]

Good explanation 👏 Nice voice 👍 this is on point Sir. Thank you so much 👏

[@shaiviharshad4655]

.. What do you mean by '' overlap of 0.05'' I didn't get that bit

[@TLMaths]

You want to find the values either side of 0.05

[@shaiviharshad4655]

@@TLMaths thanks so much. Your videos help a lot

[@user-ji8ir3jx9j]

ur an awesome teacher man thanks so much!!!!!!!!!!!!!

[@spaghettiking653]

Nice, stats test tomorrow so very helpful to see :)

[@eddieshearman9967]

This man saves people

[@Tmnt2407]

Thank you so much... i struggled with this but now its clear

[@mlakmohamed1900]

On 17:33 you know for when its its a two tail test and the p is not equal to the 0.52 when ur working out the critical region would you always use less than/equal to I'm confused on which sign to use i have a different calculator so i have to work it out by trial and error for the overlap and i cant tell which sign

[@TLMaths]

You should always use cumulative probabilities (so less than or equal to if looking at the lower end, and greater than or equal to when looking at the upper end).

[@sheralaine8403]

MUCHOOOOOOOOOOO GRACIASSSSSSSS I'VE BEEN TRYING TO FIGURE OUT HOW TO DO THIS FOR LIKE 6 MONTHS

[@Absman09]

Incredibly helpful! Thank you very much

[@arsalasif9731]

You are a great teacher sir

[@ismailrahman2679]

Helllooo jack. Perfect video. I got one problem however, the calculator doesn't allow you to go over n = 45. What do you do if n is 50 then for example??

[@TLMaths]

You don't need to type them all in - just try some numbers out. So If X~B(50,0.8) and H1:p>0.8, for example, then first do 50*0.8=40 (this is the mean). Then I would only need to look at values of X larger than 40 on my calculator, so that reduces the number I need to type in. Hope this helps

[@imank3007]

think you just saved my AS wow thank you

[@jamespound1743]

who’s got a test tomorrow then?

[@FrancisKaldunski]

You’re a legend mate

[@owaismohammed1558]

wow helped so much thanks

[@samuelmackay6260]

life saver you are a true hero

[@ethanwykes9607]

Tysm. This wouldve taken me days to figure out on my own rn 😂

[@taehyungshabibti]

thank you so much

[@Nethmi3]

this was very helpful thank you sir 💜

[@ibrahimmiah562]

could you explain how to do this on a casio fx-cg50 calculator pls?

[@TLMaths]

I'm afraid not - I don't use that calculator

[@nikki2423]

Great video!

[@dannyroome4973]

Hey there, I still don’t understand why you increase the number by 1 when looking at a probability that is greater

[@TLMaths]

The table generated shows P(X less than or equal to a) In order to find P(X greater than or equal to 4) you need to do 1 - P(X less than or equal to 3)

[@ReblazeGaming]

@@TLMaths Why do you increase it by 1 though like at 13:24 you said the overlap occurs between 13 and 14, but instead of doing for 13, 1 - P(X less than or equal to 12) you added 1 to them and did it for 14 and 15 instead

[@TLMaths]

So we're looking for the overlap of 0.975, which is between 13 and 14, agreed. We need to find two probabilities that are greater than or equal to, that are either side of 0.025. One of these probabilities needs to be greater than 0.025 and the other needs to be less than 0.025. If you worked out P(X>=13), this is equal to 1 - P(X=14), this is equal to 1 - P(X

[@davidoloughlin7612]

2:21 why can the binomial only take on the values 0-10 I thought the information given only meant that there’s 10 trials and the probability of success is 0.3 how do we know all the possible outcomes from that?

[@TLMaths]

X~B(10,0.3) tells us that there are 10 independent trials, with the probability of success being 0.3. This means we can either have 0 successes, 1 success, 2 successes, ... up to 10 successes. If there were 10 trials, there's no way you could have 11 successes.

[@davidoloughlin7612]

@@TLMaths thank you I forgot the outcome were the numbers of successes nd with a given number of trials of course this will be the maximum

[@AlEx-ro7kd]

ahhhh i'm having trouble calculating the probabilites on a table on the fx-cg50. I've looked at other videos and got it working but got different values on what you had

[@AlEx-ro7kd]

ooooh nevermind, it seems like its like a cumulative of the data, is there a way to set this up in the calculator?

[@TLMaths]

I'm sorry, I have never used the fx-cg50. What you're probably having difficulty with is the difference between binompdf and binomcdf. Pdf is for particular values, for P(X=a), while Cdf is cumulative values, for P(X

[@AlEx-ro7kd]

@@TLMaths no problem, i watched a video of someone doing it and it worked,so for anyone whos struggling use this: " For your purposes, what you need to do is 1) In list 1 - enter 0,0,0,0,0,0,0,0,0; 2) In list 2 - enter 0,1,2,3,4,5,6,7,8; 3) create a BPD using list 2 as input values, and list 3 to save the results; 4) Create a BCD, using L.List = List 1, U.List = List 2, and save results to List 4. Can you let me know if this makes sense to you and whether it now gives you the correct results?"

[@joewaugh252]

I've got an fx cg50 too. If you've got one, you don't need to mess around with any tables or anything. You literally just use the Hypothesis test function in the stats menu and input the data from the question into your calculator and then it gives you the answer. You don't get any marks in the exam for doing all this table stuff anyway. You only have to bother with using a table if you have a cheap calculator.

[@sajidashabbir1920]

Al Ex please mention me that video because my values are different from the values of the sir.

[@faizah953]

THANK YOU!

[@hedislimanesintern2382]

In Edexcel S2 will there be any questions that require us to calculate probabilities using our calculators instead of using the probability tables in the formula sheet? Or consequently might there be any questions that require probabilities to be calculated that surpass the limits of the probability tables? So eg: a binomial distribution probability where n is 75 and p is 0.75?

[@TLMaths]

What do you mean by S2?

[@hedislimanesintern2382]

@@TLMaths By S2 I mean the Edexcel A level maths module 'Statistics 2'

[@TLMaths]

Edexcel S2 hasn’t existed since 2017 when the current specification came in. A-Level Maths is no longer modular.

[@hedislimanesintern2382]

@@TLMaths I am sitting the module exam in January. The code is WST02 Statistics 2. Having had a second look it might be Pearson and not Edexcel. Sorry I'm not too familiar with all these exam versions.

[@TLMaths]

Apologies, that’s the Edexcel International A-Level. I’m afraid I really don’t know much about that specification at all. I really only know about the England specifications.

[@JK-vm7yo]

For the second one Did u align the numbers correctly cos I got the numbers from the list and put the binomial into my calc but the values are 1 above from yours- so When u say u got 0.0152 from X is less than or equal to 6 I get 0.0152 from 7???

[@TLMaths]

Are you reading the x value from the x column? Unhelpfully, the classwiz has numbers on the left hand side too, which can confuse things. You may be seeing 7 then 6 then 0.0152

[@samchurch9579]

The sound of the pen hitting the whiteboard makes me feel dangerously content.

[@user-jq3qt8no7h]

Hi someone told me that you can check your Binomial Expansions by ‘plotting each line as a graph and checking if they overlap’ I don’t get what they mean do you know how to do what they mean?

[@TLMaths]

Did you mean binomial expansions? Or did you mean the Binomial distribution? You could draw the binomial distribution, but it would be very fiddly as a checking tool.

[@KARMA-qt6vn]

8:30 do need to find both for >= and

[@TLMaths]

The 2nd example is one-tailed, so there is only one critical region to find.

[@adamfn5171]

your amazing

[@auser748]

Finally i got this

[@TABAssassin]

Do only two tailed hypotheses have two potential critical regions?

[@TLMaths]

Yes

[@pumkineater5593]

So when p=\, you do the lower tail as P(X=x)?

[@TLMaths]

As far as I'm understanding your question, yes

[@pumkineater5593]

Jack Brown thanks for your help.

[@coolyoutubers8224]

I have the CASIO fx-CG50 instead of the CASIO FX-991EX. How would I do this on my calculator?

[@TLMaths]

I don't know, I don't use that calculator

[@sijaybalchurn535]

Hello i am having some issues i have a deli calculator D82ES PLUS can you show me to calculate the values please sir its urgent

[@TLMaths]

I don't know if it can - it appears to be a basic scientific calculator. You should upgrade to the casio classwiz fx-991ex (you will need at least this for A-Level Maths in England)

[@safamerchant3529]

Which one is this Binomial CD or Binomial PD for the list function?

[@TLMaths]

CD

[@dr.shawboss]

thanks so much i am always ask my selfe that why chai-square valeu is almost posative? please can you helpe me aboute this question

[@TLMaths]

What do you mean by almost positive? I don't understand

[@apatchy0664]

For a two tailed test is it always made less than the significance level or can it be sometimes the value that is closest to the significance level? Would that be stated in the question?

[@TLMaths]

No you're always looking for less.

[@lassassinraider]

I just used 0.05 for the last one

[@lassassinraider]

Why do you half it

[@TLMaths]

The significance level is the probability of rejecting the null hypothesis when in fact it is true. If you're doing a two-tail test, the significance level is shared out between both tails evenly, as COMBINED this is the probability of rejecting the null hypothesis (if the probability hits either extreme).

[@TheALevelMathsTutor]

Thanks for this Jack. I've always done this on the CG50 which has inverse binomial so never bothered to learn it on the Classwiz (until now as I had to do it with a tutee). My god it's laborious. Is there no way to populate the list other than typing them all in?

[@TLMaths]

Nope. Didn't know you could do inverse binomial on the cg-50 - only had one for a couple of weeks so still learning what it can do.

[@TheALevelMathsTutor]

@@TLMaths Yup. Enter the area (0.05 or 0.95 depending on the tail) and voila...last value in the acceptance region. Check out the bcd function as well - none of that subtracting from 1 nonsense for P(X>...).

[@TLMaths]

Problem is that in order to find the critical region, you must show the probabilities either side in order to score full marks. So I don't see how the inverse binomial would be of much use in an exam.

[@TheALevelMathsTutor]

@@TLMaths you are correct that bcd would still be needed. However inverse normal tells me straight away which two I need to calculate and the values used for n and p carry through to bcd so are already set up. Gets more useful the larger n is as there would likely be more guesswork.

[@lewiscunningham4946]

@@TLMaths you can use the table function on the CG50 for the same function as the distribution on the classwiz. go to menu, table (7), then OPTN - STAT - DIST - BINOMIAL- Bcd, then type x , number of trials, probability) - EXE - then SET, start at 0, end at max num trials, then step 1.

[@ghsjgsjg53chjdkhjydhdkhfmh74]

Why do we use Binomial C.D and Not Binomial P.D for this?

[@TLMaths]

You always use CD for hypothesis testing. You’re testing whether 9 or more, or 5 or less is significant, not that whether just 9 or 5 is significant

[@tbrooke3016]

For the final question why was his significance 0.025 instead of 0.05?

[@TLMaths]

It's a 2-tail test, so the significance level is halved (so 2.5% at the lower end and 2.5% at the upper end). So you compare against 0.025 rather than 0.05.

[@tbrooke3016]

@@TLMaths oh of course, thank you. Your videos really make studying from home soooooo much easier 😁

[@yahya.m27]

Hi Jack, is it possible to submit a question to you? I have a binomial hypothesis question but I'm struggling to use your method to answer it.

[@TLMaths]

Sure, pop it here.

[@yahya.m27]

@@TLMaths test statistic: X~B(40,p) H0: p=0.3 H1: p≠0.3 Find the critical region for this test using a 2.5% significance level. Answers in textbook say X≤5 and X≥19. I got the first CR correct but for the 2nd one I got X≥20 🤔 seems like they took the value that's more than 0.0125

[@TLMaths]

@@yahya.m27 I agree with X≤5 and X≥20 P(X≥19) = 0.0147... > 0.0125, so X≥19 cannot be the critical region

[@aryanahsan4381]

you may as well be my maths teacher lol u explained it in 5 minutes whereas my teacher took more then an hour.

[@sajidashabbir1920]

Sir please guide me l have fx 991es plus and my values are different from you. What l should do or Which calculator l should purchase?

[@TLMaths]

This is the calculator I use: www.amazon.co.uk/FX-991EX-Advanced-Scientific-Calculator-VERSION/dp/B0719FWP3X/ref=sr_1_1_sspa?crid=1HZNJSK1KKMJC&dchild=1&keywords=casio+fx-991ex+classwiz&qid=1587062194&sprefix=casio+fx-991e%2Caps%2C512&sr=8-1-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExTFFHMVQ4UUpaQkdOJmVuY3J5cHRlZElkPUEwNDkzNTI4NFJPUTRVMUU0WFpHJmVuY3J5cHRlZEFkSWQ9QTAyMDAwNTkxQThVNVZMQUQxR0NZJndpZGdldE5hbWU9c3BfYXRmJmFjdGlvbj1jbGlja1JlZGlyZWN0JmRvTm90TG9nQ2xpY2s9dHJ1ZQ==

[@sajidashabbir1920]

TLMaths thanks a lot sir.

[@infinitespace1982]

19:21 Sir, that is meant to be between 6 and 15

[@TLMaths]

Yep

[@yaaseenalam2023]

how would u do the table on a casio fx-cg50

[@TLMaths]

kzbin.info/www/bejne/nn2zaqxmjd12oNU

[@beccasouthwick]

How do you do this on the Casio fx-9860GII?

[@TLMaths]

I don't know, I'm afraid, as I don't use that calculator.

[@happywheelsiamanoob1233]

How would I find the critical region when n=500, p=0.17 and significant level is 10%? I can’t take 500 probabilities on my calculator! Is there any easy methods and I’m using fx-9750ii. One tail.

[@TLMaths]

First multiply n by p, 500*0.17 = 85, so this is the expected value (the mean of the distribution). So if you're looking at p

[@happywheelsiamanoob1233]

Jack Brown what about p>0.17

[@TLMaths]

All of the probabilities I mentioned in the previous comment by the way were meant to be less than or equal to. For p>0.17, just do the same thing but from the other direction, trying numbers that are larger than 85, then by trial and error: P(X>=91) = 1 - P(X 0.1 P(X>=96) = 1 - P(X 0.1 P(X>=97) = 1 - P(X

[@happywheelsiamanoob1233]

Jack Brown thanks

[@Globalz_Haqq]

do you always use the list function in binomial cd

[@TLMaths]

I would use the list for the critical region method, yes. You'd always use cd for hypothesis testing

[@Globalz_Haqq]

@@TLMaths great thank you

[@foreignsamurai]

The Algorithm is really random recommending me this, but I don't mind learning new things.

[@akhilapasupuleti4324]

sir to find the actual significance level for the third question in this video would you do 0.0132 + 0.0097

[@TLMaths]

Yes that's right

[@lizavoloboeva3500]

Just to clarify for anyone, in his last sentence he meant 6 to 15 inclusive rather than 6-teen

[@swaggerdagger6516]

Wrong! You dont just take the one less than the significance level! You take the one closest to it!

[@TLMaths]

No, you're incorrect. It wouldn't make any sense to reject a null hypothesis when the value you're considering is in the acceptance region, regardless of how close it is to the critical value.

[@samkhurana4953]

Thank you so much.. helped a lot..