# Thread: probability of Type I error

1. ## probability of Type I error

Calculate the following errors for the following tow cases:

(a) If the cholesterol level of healthy men is normally distributed with a mean of 180 and a standard deviation of 20, and men with cholesterol levels over 225 are diagnosed as not healthy, what is the probability of a type one error?

(b) If men predisposed to heart disease have a mean cholesterol level of 300 with a standard deviation of 30, but only men with a cholesterol level over 225 are diagnosed as predisposed to heart disease, what is the probability of a Type II error (null Hypothesis is that a person is not predisposed to heart disease).

An help on this one would be great!

thanks

2. Originally Posted by That Guy
Calculate the following errors for the following tow cases:

(a) If the cholesterol level of healthy men is normally distributed with a mean of 180 and a standard deviation of 20, and men with cholesterol levels over 225 are diagnosed as not healthy, what is the probability of a type one error?

(b) If men predisposed to heart disease have a mean cholesterol level of 300 with a standard deviation of 30, but only men with a cholesterol level over 225 are diagnosed as predisposed to heart disease, what is the probability of a Type II error (null Hypothesis is that a person is not predisposed to heart disease).

An help on this one would be great!

thanks
(a) Calculate $\displaystyle \Pr( \text{Reject} \, H_0 \, | \, H_0 \, \text{true}) = \Pr(X > 225 \, | \, X$ ~ Normal $\displaystyle (\mu = 180, \sigma = 20)$.

(b) Calculate $\displaystyle \Pr( \text{Accept} \, H_0 \, | \, H_0 \, \text{false}) = \Pr(X < 225 \, | \, X$ ~ Normal $\displaystyle (\mu = 300, \sigma = 30)$.