Idea behind hypothesis testing | Probability and Statistics | Khan Academy

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Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

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[iman]

For people wondering the calculations to the probability of accuracy, it is done as such:
For 100% accuracy, probability is (99/100)^100; (//the result is multiplied by 100 to convert to percentage)
For 99% accuracy, probability is (99/100)^99 * (1/100) * 100; (//the 100 at the end denotes 100 possible ways the one filing outcome can be arranged. It is the same as 100C99 for possible ways of arranging the success outcome or 100C1, both = 100)
For 98%, P= (99/100)^98 * (1/100)^2 * 100C98
For 95%, P= (99/100)^95 * (1/100)^5 *100C95; (//can also be written as (99/100)^95 * (1/100)^5 *100C5 )

[Andrei]

Unbelievable explanations! I must say that the Khan Academy has an incredibly intuitive and simple way of explaining these concepts. If University professors used your examples in class, graduates would be a whole lot brighter. Thank you!

[asmomair]

I have been fighting very very hard to understand the reason behind rejecting the null hypothesis even though I went through all those lectures explaining the process of deciding significance level, p values etc almost thousand times! But O my God, all this time I was missing a simple trick here which Mr.Sal explained so intuitively! Oh Sal I am forever in deep love with you! You have made my life so enjoyable and my quest for knowledge so easily reachable! May Allah bless you and your family!

[DBHELPSPOT]

What device are you using this video on? Also, is it an app?  I like the accuracy of your writing and the space you seem to have.

[alxbrooks]

for those that may be curious...the percentages are based on the binomial distribution formula, so 98 accurate tests would be simplify the first expression to get (100*99)/(2) and you can go from there.

[chibi_undercover]

My brain hurts from all those arbitrary calculations

[minxxdia]

this video makes it all so intuitive, loved it!

[matheusmf]

Maybe this can help:
The equation used to calculate those probabilities is:
P(k;n;p)=P(X=k)=(n k) x p^k x (1-p)^(n-k)
(wikipedia)
where:
n= number of trials
k=expected number of successes
p=probability of each success
what means: I want to know what is the probability of getting exactly k number of successes in n trials, given that each trial has a probability p to occur. This is a boolean probability, what means that the result will be always two possible possibilities. Ex. yes/no, true/false...
In this equation you have 3 terms:
Binomial (n k): is a term that means that you have a combinatory probability, with unordered permutation of k in n, without reposition
p^k: the cumulative percentage. Think like: I want this happening p% and p% and times. Remember "and" means "times"(x) and "or" means "plus" (+).
(1-p)^(n-k): this term means that after having k successes, now you want to have the opposite result, what means (1-p) of probability that result to occur, in (n-k) times ( the rest of trials lefting for n out of k). Again, "and" means "times".

[shivanshsharma]

Thanks brother...now i understand logic behind p-value..👍

[MrShysterme]

Typically, given the example, you'd sum all prob. from 95 down to 0.  That is why in hypothesis tests you usually think in terms of "a value this size or smaller", etc.  The easier way to sum would be to subtract from 100 the sum of prob. scores from 100 to 96.

[wailkhennous]

thought this will be a simple explanation about hypothesis testing

[luistato]

Lol, just discovered that there is a 37% chance that my sperm escaped the prison of condoms.

[warpiwarpi]

Thanks Sal for great videos, however you have made me too smart with all the videos and exercises of combinatorics :) At 2:38, you say and write that 97/100 is 6.0% but it is infact 6.1%. (=0, 99^97*0, 01^(100-97)*FACT(100)/(FACT(100-97)*FACT(97))).

[idknuttin]

how did he calculate the probabilities from 1:58 to 3:33?

[AdamShaiken]

I'm tasting(discerning) a distinct similarity to Chi square statistical analysis.

[tommyx]

until 3:04 it not have full explaination

[KodiBrehdon]

Say me please, what program are you using to make drawings? Thank you.

[bagourdarthur]

Thanks for the video !
I noticed something strange (or not):
P(accurate 98/100)
P(accurate 98/100)=3*P(accurate 97/100)
P(accurate 97/100)=4*P(accurate 96/100)
etc
Isn't it strange ?
If not, is someone able to explain me why please ?

[wolf]

What program do you use to make these drawings?

[rahulvaswani]

What probablity video is he talking about ? Could someone please link me