Answer to Question #278110 in Statistics and Probability for Shaon

Question

In class I explained how to calculate the probabilities of making a Type I error when the decision rules were 25 mpg and 26.50 mpg respectively. Now, under the same condition that n=30, calculate the probability of committing a Type II error in the gasoline experiment if the true with the additives = 25.750

Answer 1

A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one accepts a null hypothesis that is actually false.

for $\mu=25,\sigma=2.4$ :

$z=\frac{25.75-25}{2.4/\sqrt{30}}=5.48$

probability of committing a Type II error:

$P(z<5.48)=1$