Thread: Hypothesis testing

The producer of an electric machine wants to make a test to see how many of their machines that are working correct. The hypothesis are the following:

: the proportion of defect machines is at most 8%
: the true proportion of defect machines is more than 8%

The producer decides to reject if the sample proportion of defect machines are more than 12%.

i) If we draw a sample of 100 machines, then what is the probability of making a type I error?

I'm thinking of a Z-transformation.





And then I look up P(Z>z) in a table. Is that correct?

ii) If we know that the true proportion of defective machines is 15%. Then what is the probability of a type II error with a random sample of 100?





Since this will be negative, I look up the probability that Z(<-z) in a table. Do I think in the right way?

Thanks a lot for your help.

Originally Posted by mirrormirror

The producer of an electric machine wants to make a test to see how many of their machines that are working correct. The hypothesis are the following:

: the proportion of defect machines is at most 8%
: the true proportion of defect machines is more than 8%

The producer decides to reject if the sample proportion of defect machines are more than 12%.

i) If we draw a sample of 100 machines, then what is the probability of making a type I error?

I'm thinking of a Z-transformation.





And then I look up P(Z>z) in a table. Is that correct?

ii) If we know that the true proportion of defective machines is 15%. Then what is the probability of a type II error with a random sample of 100?





Since this will be negative, I look up the probability that Z(<-z) in a table. Do I think in the right way?

Thanks a lot for your help.

this looks OK, for the second case as is negative you want for your probability, if that makes any sense?

.