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## Statistics and probability

### Course: Statistics and probability>Unit 12

Lesson 1: The idea of significance tests

# Simple hypothesis testing

Sal walks through an example about who should do the dishes that gets at the idea behind hypothesis testing. Created by Sal Khan.

## Want to join the conversation?

• Isn't that independent event? Sal
no matter how many times he pick, still got 3/4 chance • how do you find/tell the hypothesis to plan a statistical investigation? like " a psychologist wants to look at the factors that may affect memory. She thinks gender is likely to be a factor, that is, males and females might be different.How could the psychologist test her theory? Write down any factors that you think might make a difference to memory." Do you have any simple methods on understanding this topic?? • Why can't we solve this problem using P(Bill not picked) = 1 - P(Bill get picked)?
P(Bill get picked) = 1/64. If we use that we get answer as 63/64? • @2.45, why did you multiply the probability i was thinking it show be add ?.. why can't we add the probability nd why it should only be multiplied?
look: in other way, can the question be re-framed as, what is the "total" probability of bill not picking ? so its "total" so i thought it is addition. but correct me if my intuitions are wrong.. • We add probabilities in different circumstances than we multiply them. In this case, we multiply because we are finding the odds of several various independent events happening. For example, if we were to toss two coins, the odds of the first coin coming up heads is 1/2. The odds of the second coin coming up heads is also 1/2. How do we find the odds of both coming up heads? We multiply the probabilities, as there is a 50% chance of the first coin coming up heads (in theory, one out of every two times the coin will be heads). Therefore, in the universe of first-coin-flip-heads, 1 out of ever 2 flips there will theoretically come up with a second head. Overall, then, 25% of the time we will get two heads.
I hope that was a little bit helpful.
• Does anybody know why 3/4 though?
(1 vote) • Wouldn't the older brothers chance of being selected each night be 1/4 rather than 3/4? There is a 1 in 4 chance he is selected each night. Wouldn't 3 in 4 be the chance that anyone but him be selected? It's possible I missed part of the premise.
(1 vote) • I don't manage to see the link between rejecting the hypothesis and the low probability of the observed results.
Using the Alien problem.
A) 20% of the observed sample is rebellious
B) The hypothesis is that 10% are rebellious
Let´s simulate to see how likely is (A) to happen. Simulated results show that it is unlikely (A) to happen therefore i have to reject (B).? that is what I don´t get.
In my mind I have two options, (A) or (B), if (A) doesn´t happen then (B) happens, but here it is like those are linked together and really don't understand where that link is. • The two are linked by an assumption that we make. We calculate the probability of A while assuming that B is actually true. That's why we reject the null hypothesis for small probabilities. We're saying, "We made an assumption, and the data we observed are extremely unlikely under that assumption, so they can't both be true. But ... the data are real, and our assumption is, well, and assumption, so we'll believe the data. That makes our assumption wrong."
• Isn't there a 100% that at least one child hasn't been picked after 3 days?
(1 vote) • I don't understand why Bill's chance of not getting picked 3 nights in a row is 42%, shouldn't it be 1/4 because there are four siblings, and if one of them gets picked randomly every night, then Bill not getting picked is a 3/4 chance, but it's a 1/4 chance because his chance of getting picked on Day 1 is 1/4, his probability of getting picked on Day 2 is 1/4 and his probability of getting picked on Day 3 is 1/4, because he's 1 of 4 siblings, therefore 1/4. I don't understand, can someone help?
(1 vote) • You are right in that Bill's chance of getting picked any particular day is 1/4. Also that makes his chance of not getting picked any particular day 3/4.
But here, we're not finding the probability that Bill is picked on the fourth day, we're finding the chances that he didn't get picked any of the first three days.
What would you put the chances of someone scoring a basket from half court? If they're good say maybe 10%.
But what would you put their chances of doing it 10 times in a row, or 20? Doesn't it naturally seem like scoring a basket from half court 20 times in a row is much less likely than doing it on a particular attempt?

Same thing here. 3/4 is the probability that Bill isn't picked any particular day. But when he isn't picked the first day, not the second day, not the third day? That becomes (3/4)*(3/4)*(3/4)=27/64=42% approx.
He doesn't get picked 12 times? (3/4)^12.

Sorry if the basketball reference I used didn't have the right terms. But I hope that clears up some stuff.

Cheers! 