Is this right.

#1
You have an srs of size n=15 from a normal distribution with standard deviation=1. You wish to test Ho: u=0 and Ha: u >0. You decide to reject Ho if the sample mean =0.6005 and to accept Ho otherwise.

A. Find the probability of a type I error. That is, find the probability that the test rejects Ho when in fact u=0.

B. Find the probability of a type II error when u =0.61. That is, find the probability that the test accepts Ho when in fact u =0.61.

C. Find the probability of a Type II error when u=1.


Heres what I got, pretty sure I did this wrong.

A. The probability of a type I error is 0.50.

B. 0.6005-.61/ (1/sqrt 15)= -0.036 so 1-.4840 = .52

C. 0.6005-1/ (1/sqrt15)= -1.54 so 1-.0618= .94
 

JohnM

TS Contributor
#2
You were actually pretty close.

A. Here, just find the rejection region.

z = (.6005 - 0) / (1/sqrt15))
then find the area beyond z

For B and C, you did the opposite. The correct answers are .484 and .0618, because a Type II error represents the area under the curve in the "acceptance" region.

Remember, Type II error is the failure to reject Ho when in fact it is false.