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

Question:
Gigi's Pizza regularly surveys its customers. On the basis of these surveys, the management of the chain claims that at least 75% of its customers rate the food as excellent. A consumer testing service wants to examine the claim by asking 460 customers to rate the food. Seventy one per cent rated the food as excellent. Is there enough evidence at the (a) 5% and (b) 1% level of significance to reject management's claim?

[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!

[somdevdeora]

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.

[Jeffkingson]

this guy is one of the best teachers on youtube.

[aviejaypaul]

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?

[swaaamii]

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

[anassameseabroad]

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

[wenukagunarathna]

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.

[aadhusri]

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

[dicspanner]

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

[mostafagharbawi]

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

[mostafagharbawi]

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.

[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”

[steyndewet]

Thanks so much - these vids are really helpful.

[kostiantynpalianychko]

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?

[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?

[nogamenolife]

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)?

[ntokozophiri]

I don’t understand why we using (0.25)

[benbailey]

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

[pattarapolsumreddee]

Thank you. If np and nq <5 can we use the formula for test statistic and apply this method?
I am asking since I want to use this test but my n is not large due to price of sample for QC of products purchased, eg n=10 from 150 products. My p is 0.10

[taladiv]

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