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Hypothesis testing and p-values | Inferential statistics | Probability and Statistics | Khan Academy

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Hypothesis Testing and P-values Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/hypothesis-testing-with-simulations?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/one-tailed-and-two-tailed-tests?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Missed the previous lesson? https://www.khanacademy.org/math/probability/statistics-inferential/margin-of-error/v/margin-of-error-2?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics 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! About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Probability and Statistics channel: https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
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Text Comments (598)
Minhee Kim (6 days ago)
This lecture definitely helped me a lot.
Monir Real Viva (6 days ago)
How can find 0.003
Yatin Arora (8 days ago)
explained very well thank you for clearing my doubt
rero chan (9 days ago)
م فهمت 😭💔
Sunny Yoda (15 days ago)
What? I am so confused.... and screwed
hubert1990s (17 days ago)
so puzzling part about sd (6:40). the instruction says "with a sample sd of 0,5", then he says "best estimation of sampling distribution standard deviation" - does it mean population distribution or what?
James Bekurs (17 days ago)
THANK YOU!!!! I was struggling to grasp this concept in a practical sense, and your video helped me connect the dots.
Cristal 24678 (24 days ago)
I’m a third stage medical student why I should study statistics 🤯🤯😤🤐
denzel (29 days ago)
i am going to reject i am going to reject i am going to reject
Halle Finn (1 month ago)
isn't it a t score because you're taking the mean? also none of the conditions were met or even tested...
falcon lover (1 month ago)
Does anyone know the difference between sample standard deviation and standard deviation of sampling distribution???
Light Yagami (1 month ago)
love you khan
Isabelle Contreras (1 month ago)
Thanks a lot! This video really explains hypothesis testing in a very simple way.
jiabin luo (1 month ago)
sorry. why it's 99.7%? how to calculate. Thanks
easybuckets (1 month ago)
it's part of the empirical rule which states 99.7% of the data will fall within 3 standard deviations of the mean
ig ig (1 month ago)
thank you you helped me a lot in fact, you save me you are a very great teacher
Krishna Kumar (1 month ago)
I did not understand, why did we chose to look for values >3 std-devs instead of <3 std-devs or =3 (in which case prob would be 0).
unknown beast (2 months ago)
guys, what does he mean by result this extreme in 9:50
unknown beast (2 months ago)
+Bioengineer thank you for taking part of your time to reply!
Bioengineer (2 months ago)
It means that the null hypothesis is unlikely to be the true population mean. The nearer the null hypothesis is from the sample mean, the greater will be it's probability to be the true population mean. But the result showed it was far away, so, as the result showed, you can reject it with a probability of 0.3% to be mistaken. There's 0.3% chance that the true population mean will be greater or equal to 1.05+3*0.05=1.2s or less or equal to 1.05-3*0.05=0.9s. As a result, there's a 99.7% chance to be 0.9<True pop. mean<1.2.
Aures (3 months ago)
I learned more in 12 minutes online than I did for 3 90 minute university lectures lol
Sheldon Tauro (3 months ago)
Could anyone explain why did we divide the standard deviation by the root of the sample size .
sephiroth (4 months ago)
i am from multimedia design, doing phd now in social science n have to do quanti, n learn statistic, n here i am, some school level statistic lesson..cuz i have zero knowledge on statistic..
SquidySquirts (5 months ago)
So is the P value for the hypothesis (not null) 0.97?
Salma Mohamed (5 months ago)
hey
John Dempsey (5 months ago)
Take a shot every time he repeats himself
Viswanath Viswanath (5 months ago)
We already given sample standard deviation is o.5, why we have to estimate ?
abc def (6 months ago)
It would be better if you stop repesting yourself
Plague Doctor (6 months ago)
How on earth are you teaching this if you don't even know that the plural of hypothesis is hypotheses (hypothe-sees, like see with your eyes)
Spurgeon Green (6 months ago)
Eternally grateful
duc anh duong (6 months ago)
so where dose 99.7/% come from?
Ryan (6 months ago)
Wouldn't that be .03 not .003...
Kashyap Iyer (6 months ago)
shouldn't the p-value be 0.15%? as we have to consider the part only on the left side of the mean, that is 1.05, and not 1.35...
D.F (7 months ago)
Can i borrow your mind for tomorrows exam?
Joana Jenkings (7 months ago)
Can someone tell me when I'm ever going to use this in my everyday life?
MarMar Meows (7 months ago)
I’m gonna fail my statistics class
Lloyd Carmona (7 months ago)
Thank you
Selena Rodriguez (7 months ago)
What about the time saying if there's enough or not enough evidence?
Hannah H (7 months ago)
Your videos make everything so much clearer! Thank you so much for sharing 😊
Misaki Ichigo (7 months ago)
how did you know p value is 0.03% what's the relation with 3 std dviations
Sarah Moody (7 months ago)
thank you༼☯﹏☯༽
Jordan - (7 months ago)
Why dont we divide the 0.003 by 2 as we are only looking at one side of the bell curve?
Sizwe Mbokazi (7 months ago)
i need GPS for this
Mark Elrod (8 months ago)
Look at it this way, the null is saying that "there is no way on earth that the average is any value but 1.2 seconds." Then, assuming that is true, we do some math and figure out that if the drug indeed did have no effect, and we randomly sampled mice 100 times, it there would be a 0.3% chance that some of those mice had response times of 1.05 seconds. So it would be super improbable to get a value of 1.05 seconds. Now....rewind back to the problem. We were told that the scientist not only had mice with a response time of 1.05, but even better, that was his average response time! This means that it is crazy to think that the drug had no effect, because if it didn't there would only be a 0.3% chance we got a value of 1.05 seconds.
SA 3 (8 months ago)
He say that we assume that 0 hypothesis is true. What does or assumption change in the calculations? would we make other calculations if we assumed the alternative hypothesis was true?
Fun Uber Games (8 months ago)
Legend has it that P.E.T.A was up and arms about this video.
Jagroop Singh (8 months ago)
Nvm. I'm just gonna skip this question tomorrow
Małgorzata Górska (8 months ago)
Okay, I don't get why you'd choose to reject the null hypothesis if the probability of getting the extreme result of the alternative hypothesis is only 0.3%.For me, if something has 99.7% chance of happening, then it is almost certain. I feel like I'm stupid here.
Katherine G Carpio (8 months ago)
This legit didn’t help me at all. I don’t get it...
thatnolan (8 months ago)
Yes! Thank you!
MegaMsc123 (8 months ago)
This guy is boring AF
tomlinzombie (8 months ago)
My stats final is at 6:00.... I still dont get it....
Rose B (8 months ago)
i dont understand how it differs from a value?
CK (9 months ago)
5:18 it's not the standard "deviation" of the sample distribution but standard "error" of the sample distribution. se=s/sqrt(n)
Pirilani Banda (9 months ago)
but isnt it when we are not given the population standard deviation we then use the T table? am abit confused
SheStillRuns (9 months ago)
SALMAN KHAN IS THERE ANYTHING THAT YOU DON'T KNOW? EVEN GODS DIVIDED THE COSMOS AND THE ELEMENTS AMONGST THEMSELVES. SAL KHAN, GOD OF PAN-OLOGY.
Matin Sayed (9 months ago)
Thank you Khan!! You're the best. So much explained under 15 min - incredible!
Prinz von Kirchberg (9 months ago)
Wrong. 99.7% of the prob is within 2.75 deviations...
Nicolai Or Die (9 months ago)
why isn't the sample standard deviation what the video calls the standard deviation of our sampling distribution? I understand that s = 0.5 and that std dev of x bar = 0.05 but i just wanna understand the difference so i know how to clock it on the exam
Peter Uhd (9 months ago)
Thanks dude, clear and easy to follow
Daniel Murillo (9 months ago)
This is an awesome explanation.
rtong12 (10 months ago)
You guys are awesome...even for this middle aged professional...education never ends 😀
Abhay Dhotrekar (10 months ago)
0:38
Rubi Goswami (10 months ago)
the sample's standard deviation is already given to be 0.5 seconds. Why do we calculate it again as 0.5/sqrt(sample size)?
Bretta Sipa (10 months ago)
Why are you not using the one sample t-test? I don't understand why you chose this method?
Maanya P (10 months ago)
why are you not using t statistic when you sigma is not known, it will lead to more accurate conclusions.
Naz Kauser (10 months ago)
can somebody tell me what is the reason why a author would not add a p value or confidence interval in his randomised controlled trial? the author already stated there is no significant difference but is there any literature I can use to back the reason of why he didn't add a p values or confidence interval in his randomised controlled trial???
Truly Fave (11 months ago)
This is one of the few khan tutorials that I didn't really understand :(
pablo escobar (11 months ago)
Khan rocks!!!
Bart de Baat (11 months ago)
Thanks
Princess Pioquid (11 months ago)
7th grader here haha!
Nur Syahirah (11 months ago)
how did u get 99.7%?
Om s (11 months ago)
4:15 why are we calculating the standard deviation of sampling distribution when it's already given in question as 0.5 seconds?? what's that 0.5 seconds?
Rayan Itani (11 months ago)
As show the table the p-value should be 0.0013.
Ceekh (11 months ago)
Hi guys, also watch videos on our channel for simple understanding of p value
Erin Saylor (11 months ago)
There's something about how this guy repeats certain key steps once or twice that just really helps me keep up with the lesson. ADHD is a b*tch.
Martin Federico (11 months ago)
This is not the way to do this.
iliadisi1 (11 months ago)
When I was undergraduate I was passing some of my exams through Khan Academy. Now I dont get it... I was expecting better explanation
RheRheBunny (1 year ago)
What's the name of this test?
Katherina Janevski (1 year ago)
I thought that we never “accept” the alternative?
Ayush Agrawal (1 year ago)
after considering the three std. deviation interval , why did u take the positive side as well? For the hypothesis to be true we need to see if reaction time is 1.05 or less with significant probability due to drugs
Ellie Cortez (1 year ago)
:c
C Ni (1 year ago)
we do not have the population standard deviation. is it because the sample size large enough to use z-test instead of t-test?
zenapsgas (1 year ago)
Id fail the test completely if I followed these steps.
Jay b (1 year ago)
Wouldn't the p value be .03/2? Alpha/2?
Kevin Shang (1 year ago)
I’m writing in 30min. If you reading this, just know I’m probably on my way to apply a job at McDonald’s. Who needs AP maths anyway?
KaiXuan Zhang (1 year ago)
got it! a good vedio
Kiran Varri (1 year ago)
well explained...thank you :)
李徐泓 (1 year ago)
There are three standard deviations he is talking about: the std of sampling distribution (of the mean) "\simga_{\bar{x}}" , the std of entire population distribution "\sigma" and sample std "s". (1) When the number of examples in a sample is large, "s" will be very close to "\sigma". This is pretty easy to understand, more sampling, closer to the true distribution. (2) "\simga_{\bar{x}}" means another thing, 100 examples as a sample, we compute the mean of these 100 examples; then we take another 100 examples and compute the mean; we do a lot of times; we compute the std of these means, this will be the std of sampling distribution of the mean. This is what he wants to compute and his computation is correct. (3) why computing "\simga_{\bar{x}}"? because all from beginning, all he compute is the mean. 1.2 is the mean, 1.05 is the mean. He tries to determinate how 1.05 is from 1.2. And the distribution of the mean is also a Gaussian distribution but with a smaller std, which we didn't at first but we can compute it by the formula given in the video, so it's 0.5 / sqrt(100) = 0.05. (4) why 0.03 not 0.015? I think it's because the hypothesis here is u != 1.2, not u < 1.2. So the extreme situation like getting 1.05 has the same probability as getting 1.35. Hope this helps.
Matthew James (1 year ago)
Why am I paying my University to learn 95% of content via YouTube...
Aaron Staton (1 year ago)
I know he wanted a positive number, but he didn't perform the proper equation. It should have been (M-u) / (simga / sr of n), not (u-M) / (sigma / sr of n). So the correct statement is: (1.05 - 1.2) / (0.5 / sr of 100) = -3. This mistake can cause an incorrect answer in a one-tailed test, or one where the + and - signs are important.
blessedspear (1 year ago)
why is it 0.003 instead of 0.0015
aitai sakura (1 year ago)
I kinda get it but dont get it..
Ashraful Imran (1 year ago)
In the two sample test. which one will be Population-1 & which one will be Population-2. How can be selected 1& 2?
Alex Ander (1 year ago)
Thanks, got it! (: KhanAcademy is way more effective than my uni lectures
Jeterify (1 year ago)
This is so helpful. Thank you!
somak maitra (1 year ago)
This video is not very clear about z test or Ho Ha accept reject please split and make 2 videos.
Asif H Tamim (1 year ago)
I've spent whole day to understand this and this video my concepts clear within 10 minutes. You're awsome Sal. <3 From Bangladesh.
Ornella Flavien (1 year ago)
i dont get why were finding the sample standard deviation when they gave it in the question!!!
sir I have a problem of stats but I am not getting how to solve problem is two batches of animals each are given test of inoculation , one batch was inoculated and the other was not the numbers of dead and surviving animals are given in the following table for both cases can the inoculation be regarded as effective against the decease at 5℅ level of significance dead. survival. total inoculated. 2. 10. 12 non inoculated. 8. 4. 12 total. 10. 14. 24 can please anyone solve this for me
K Mystry (1 year ago)
where is this vidoe on khan academy? the vidoes there are too simple and this one has more meat.....
Melissa (1 year ago)
@9:38 how did he derive that the area is 99.7%? and the other two pink areas are 0.3%?
Fanrong Meng (1 year ago)
i have watched this video for many times, but i still don't figure it out when to accept H0. "let's assume that null hypothesis is true, if the null is true, what is the probability that we would have gotten these results. if the probability is really small, H0 is rejected " why H0 is rejected? If H0 is true, then u =1.2s, and possibility of u=1.05 should low, that means H0 is correct. i hope some guys understand what i am saying and can help me with that.

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