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What does the p-value represent in hypothesis testing the probability?
In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.
What is the probability of a biased coin landing on heads?
2/3
A biased coin has `2/3` probability of landing heads.
How can you tell if a coin is biased?
There are two ways to determine if a coin is biased or fair. The most common way is to flip the coin a bunch of times and see what fraction are heads. If you only flip it 10 times and get 3 heads, there is little to conclude. But if you flip it 1000 times and get 300 heads, it almost certainly is biased.
What is the probability that you get heads if you flip a biased coin where heads comes up 4 times as much as tails?
1/16
N=0: There is only one possible outcome that gives 0 heads, namely when each flip results in a tail. The probability is therefore 1/16. N=4: There is only one possible outcome that gives 4 heads, namely when each flip results in a head. The probability is therefore 1/16.
Which is the null hypothesis for tossing a fair coin?
For tossing a fair coin (which is what the null hypothesis states), most statisticians agree that the number of heads (or tails) that we would expect follows what is called a binomial distribution.
What is the probability of the null hypothesis?
The red outlined bars show the probability distribution of the number of heads under the assumption that the null hypothesis (fair coin or p=0.5) is true, while the blue shaded bars show the probability distribution of the number of heads under the assumption that the null hypothesis is false (and p=0.7).
Can you test the null hypothesis that heads are just as likely as tails?
Suppose I say that in order to test the null hypothesis that heads are just as likely as tails, I’m going to toss the coin 100 times and record the results. Carrying out this experiment, I find that I saw 55 heads and 45 tails. Can I safely say that the coin is true?
What is the probability of a coin being thrown 900 times?
If the coin is unbiased then the probability of ‘heads’ is 1 2. Therefore, the number of heads thrown in 900 tries, X, has a Binomial(900, 1 2) distribution under the null hypothesis of a fair coin. So, the p -value – the probability of seeing a result this extreme or more extreme given that the coin is far, is