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edit approved Mar 1, 2023 at 11:32

I can't help you with the first part of your quesitonquestion, but this is how I explain the second to my students:

I stand at the front of the class, and I flip a coin. Each time I do so, I look at the coin and I tell them that it has come down heads. I do this 10 times. At first they pay little attention, but by the 10th flip thatthey are all amused, and have obviously figured out that I am lying to them. How have they done this? Well, if I were telling the truth, itsit's very unlikely that a fair coin would come down heads 10 times in a row.

What they are doing is ana hypothesis test. Their (implicit) null hypothesis is:

H0: there is a 50% chance of heads and 50% chance of tails, and that I am telling them which it is each time.

The likelihood of getting 10 heads in a row is 1/1,024 (or the liklihoodlikelihood of getting 10 of the same in a row is 1/512). As this is a very small probability, they decide to reject H0. They all do this without having come across hypothesis testing before.

Now consider a different situation.

I toss the coin, look at it, and tell them either heads or tails. I do this and tell them 4 heads and 6 tails. I do this irrespective of which way the coin actaullyactually comes down.

4 heads and 6 tails is a perfectly unremarkable result from a fair coin, and so they have no evidence to accuse me of lying again. However, I have lied. It doesn't matter how the coin comes down, I always tell them 4 heads and 6 tails. So while they have no evidence to reject the null, itsit's also not really evidence to accept it either.

I can't help you with the first part of your quesiton, but this is how I explain the second to my students:

I stand at the front of the class, and I flip a coin. Each time I do so, I look at the coin and I tell them that it has come down heads. I do this 10 times. At first they pay little attention, but by the 10th flip that are all amused, and have obviously figured that I am lying to them. How have they done this? Well, if I were telling the truth, its very unlikely that a fair coin would come down heads 10 times in a row.

What they are doing is an hypothesis test. Their (implicit) null hypothesis is:

H0: there is a 50% chance of heads and 50% chance of tails, and that I am telling them which it is each time.

The likelihood of getting 10 heads in a row is 1/1,024 (or the liklihood of getting 10 of the same in a row is 1/512). As this is a very small probability, they decide to reject H0. They all do this without having come across hypothesis testing before.

Now consider a different situation.

I toss the coin, look at it, and tell them either heads or tails. I do this and tell them 4 heads and 6 tails. I do this irrespective of which way the coin actaully comes down.

4 heads and 6 tails is a perfectly unremarkable result from a fair coin, and so they have no evidence to accuse me of lying again. However, I have lied. It doesn't matter how the coin comes down, I always tell them 4 heads and 6 tails. So while they no evidence to reject the null, its also not really evidence to accept it either.

I can't help you with the first part of your question, but this is how I explain the second to my students:

I stand at the front of the class, and I flip a coin. Each time I do so, I look at the coin and I tell them that it has come down heads. I do this 10 times. At first they pay little attention, but by the 10th flip they are all amused, and have obviously figured out that I am lying to them. How have they done this? Well, if I were telling the truth, it's very unlikely that a fair coin would come down heads 10 times in a row.

What they are doing is a hypothesis test. Their (implicit) null hypothesis is:

H0: there is a 50% chance of heads and 50% chance of tails, and I am telling them which it is each time.

The likelihood of getting 10 heads in a row is 1/1,024 (or the likelihood of getting 10 of the same in a row is 1/512). As this is a very small probability, they decide to reject H0. They all do this without having come across hypothesis testing before.

Now consider a different situation.

I toss the coin, look at it, and tell them either heads or tails. I do this and tell them 4 heads and 6 tails. I do this irrespective of which way the coin actually comes down.

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created Feb 28, 2023 at 16:08

Ian Sudbery

I can't help you with the first part of your quesiton, but this is how I explain the second to my students:

I stand at the front of the class, and I flip a coin. Each time I do so, I look at the coin and I tell them that it has come down heads. I do this 10 times. At first they pay little attention, but by the 10th flip that are all amused, and have obviously figured that I am lying to them. How have they done this? Well, if I were telling the truth, its very unlikely that a fair coin would come down heads 10 times in a row.

What they are doing is an hypothesis test. Their (implicit) null hypothesis is:

H0: there is a 50% chance of heads and 50% chance of tails, and that I am telling them which it is each time.

Now consider a different situation.

I toss the coin, look at it, and tell them either heads or tails. I do this and tell them 4 heads and 6 tails. I do this irrespective of which way the coin actaully comes down.

4 heads and 6 tails is a perfectly unremarkable result from a fair coin, and so they have no evidence to accuse me of lying again. However, I have lied. It doesn't matter how the coin comes down, I always tell them 4 heads and 6 tails. So while they no evidence to reject the null, its also not really evidence to accept it either.