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Suppose we find a coin and wonder whether it's fair.
As a first test, we decide to flip the coin 200 times and count the number of heads,
Suppose we have a coin which we suspect comes up heads more often than a fair coin would.
As a first test, we decide to flip the coin 200 times and count the number of heads,
Suppose we find a six-sided die and wonder whether it's fair. As a first test, we decide to roll the die 100 times and count the number of times it comes up 1. The expected number of 1's is 50/3, with a variance of 125/9.
Using a normal approximation, what is the smallest number of 1's greater than 50/3 that would be extreme enough to reject the null hypothesis of a fair die?
Using a normal approximation, what is the greatest number of 1's less than 50/3 that would be extreme enough to reject the null hypothesis of a fair die?
Suppose that this die is weighted so that it rolls a 1 with probability 0.2. What would be the power of our test?
Suppose we roll the die 100 times and see 23 1's. Use the maximum likelihood value for the probability of rolling a 1 to calculate the power of the test.
Suppose a particular plant when grown outdoors has an average height of 39 in with a variance of 20 in