Hyp testing #4: testing for the population proportion, p (or π)

[@AddieInGermany]

I literally watched your Hypothesis playlist, Distribution playlist, and statistical inference playlist in 2 days. It was too much of wisdom. I need to sit back, go through my notes again. Crazy crazy learning. Thank you so much for putting so many efforts that you made them look so effortless. Thank you, sir!

[@zedstatistics]

Filing this under "you've made it all worth while". Thanks so much, AR! It's tough to know whether people actually appreciate the vids... but hearing your feedback is really nice!

[@cameronshorkey843]

@@zedstatistics We definitely DO appreciate the vids. You should be sainted for making them. Videos like this are what makes the internet one of the great inventions of history. How cool that you can learn statistics from home for fun during a pandemic. I hope you're well compensated, amigo! Do you have a Patreon page?

[@taladiv3415]

@@zedstatistics Why the f₪$& would anyone not appreciate your genuine efforts to help us all?

[@Realflawdababy]

po

[@Jeffkingson]

this guy is one of the best teachers on youtube.

[@somdevdeora8130]

you are doing a great job sir. its great to be an indian and learn from an australian without actually stepping out of home. literally helped me understand concepts which seemed daunting a while back. thanking your efforts for everything i have learned under this topic.

[@wenukagunarathna2411]

At 5:14, don't we have to divide the standard deviation by root(n) according to the CLT? At the end of the day we are talking about the distribution of "average" rating, right? or please correct me if I am wrong.

[@santoshmolgu862]

variance for binomial distribution is np(1-p), since we know the population mean, we don't need to divide variance by root(n). So the test statistic becomes np^-np/sqrt(np(1-p)). Hope that makes sense

[@aviejaypaul6568]

Hello Sir, isn't the standard deviation of a Binomial distribution given by sqrt{n*p*(1-p)}? Why have you divided p*(1-p) by n?

[@nogamenolife9182]

4:50 Why do we divide by n in there while approximation of std from binomial to normal is square root of n*p*(1-p)?

[@nogamenolife9182]

Nevermind, I'm dumb. we get that If we divide by n the square root of n*p*(1-p).

[@swaaamii]

hey, beautiful videos, I seldom comment on videos, but your videos made my work so much simpler. Thank you and cheers.

[@taladiv3415]

10:24 I truly hope that the moral and healthy choice to turn in to a Vegan restaurant would really boost their rating.

[@dicspanner8738]

question. if we are saying "at least 75% shouldn't we write our Ha as p > 75? because " at least " means 75 and above. please help me understand there

[@TranNguyen-yi5tg]

me too

[@TranNguyen-yi5tg]

maybe the teacher misread the question. he read it as "less than 75%" instead of "at least"

[@anassameseabroad5318]

You are THE BEST STATISTICIAN. The least I can say.

[@steyndewet1191]

Thanks so much - these vids are really helpful.

[@Iamsad120]

Thanks!

[@Iamsad120]

love your videos lol... just one question. since i am a newbie ... where did you get the sample proportion 71%???? there was no mention in the example given

[@aadhusri8355]

Thanks so much ! You are awesome at explaining what you have learnt.

[@mostafagharbawi3607]

For the 1% SL, we become less strict as to compare with 5%? (We allow for more extreme cases to come under accepted region).

[@JFauerbach]

Could we state the conclusion in rather different wording? “There’s enough evidence to be 95% confident that the proportion of customers rating the food as excellent is less than 75%, but we cannot be 99% sure”

[@benbailey5685]

What would you do when the CLT does not apply and np < 5

[@batatambor]

Imagine that the surveys have 4 different answers: Excellent, Good, Regular and Bad. If we want to create confidence intervals for each answer, do we need to calculate 4 different confidence intervals, considering 4 binomial answers (Excellent and not excellent, good and not good, regular and not regular and bad and not bad) or is there another way to find the intervals?

[@mostafagharbawi3607]

Hi, I just couldn’t get my head around calculating the variance: I suppose it’d be sqrt(ncap*0.71*0.29/n), where n=460, ncap=460*0.71, which clearly not the one used in the solution suggested. Please could someone help? Thanks in advance.

[@kostiantynpalianychko2195]

Thank you, watched and noted almost all your vids, top-notch content! Question: why is this Binomial distribution? Can we really say that each person's answer is a Bernoulli trial with fixed probability = p? It seems to me, that each person can have different probabilities, and only because there are many of them - we sum them up and apply Central Limit Theorem. Then how we justify calculation of standard deviation here?

[@benigntumor3366]

It's a necessary simplification of reality that allows us to build a statistical model here. Of course you're not wrong that in reality each person might have a different probability of liking the food. However if you go with that, you're pretty much stuck right from the start. How would you proceed from there? There's a famous saying in statistics which I think also applies to all sciences, "all models are wrong, some are useful".

[@mirkobruhn9841]

Hm, at 2:31 you have mu in your H0 and H1 instead of p. Is that a typo?

[@_M_D_M_]

Seems so

[@Engineer78206]

nice video, thank you sir

[@ntokozophiri2771]

I don’t understand why we using (0.25)

[@pattarapolsumreddee1053]

Thank you. If np and nq

[@apoorva3880]

I cant thankyou enough, sir.

[@whetstoneguy6717]

Mr. Justin Z--at 6.14 of the video, in the sample of 460, why did you not use 460-1 = 469 in the denominator and use a formula of the square root p(1-p)/(n-1)? I ask this because the 460 customers are just a sample. WhetstoneGuy Aug 31, 2020

[@whetstoneguy6717]

I meant to state 460-1=459. WhetstoneGuy Aug 31, 2020

[@emalynarnan2186]

How do you solve if there is no alpha or the confidence level given in the problem?

[@zedstatistics]

Well lucky you, you get to choose! (boring answer: just use alpha=0.05, that's kinda the default)

[@dicspanner8738]

ooooo i see. our claim is looking to reject the "at least 75%" meaning we want at most 75%. ok i got it

[@christophermoltisanti2970]

Arent't we seeking evidence for p > 0.75

[@ntokozophiri2771]

That’s what confuses me

[@Zeddy27182]

Too late, but we need to reject the claim that is p>=0.75 if we have enough evidence. So, that's why.

[@Franckzzz]

No, the claim is that more than 75%. This is trying to find evidence against their statement and trying to prove that it is less than 75%

[@Bangash-qi8iu]

pushing p

[@durgeshmishra9449]

Thank you Sensei!!