Type I & II erros- plz help

Quote:

Originally Posted by sclady

Problem:
John has to decide which of two discrete distributions a random variable X has. The Probability Dist. are given by the following table.

X 1 2 3 4 5 6 7
Po .1 .1 .1 .1 .1 .2 .2
P1 .1 .2 .1 .1 .2 .1 .2

John take a single observation and wishes to test the null hypotheses that Po is valid the alternative hypthesis that P1 is true. He has decided to accept the null hypo if he gets a 5, 6 or 7 and reject it.

a- what is the prob of Type I error?

b- What is the prob of Type II error?

Let $p_0$ be the probability of getting a $5,6$ or $7$ given the $P_0$ is the case, and $p_1$ be the probability of getting $5,6$ or $7$ given that $P_1$ is the case.

A Type I error is a false positive, so is the probability of getting a $5$ , $6$ or $7$ given that $P_1$ is the case.

A Type II error is a false negative, so is the probability of not getting a $5$ , $6$ or $7$ given that $P_0$ is the case.

CB