# Stats unknown variance hypothesis testing

1. Oct 17, 2007

### Punchlinegirl

1. The problem statement, all variables and given/known data

A machine produces metal rods used in an automobile suspension system. A random sample of 12 rods is selected and the diameter is measred.The sample mean is 8.28. and the significance level is 0.05. Is there strong evidence to indicate that mean rod diameter is not 8.20 mm using a fixed level test?

2. Relevant equations

3. The attempt at a solution

I tried finding the variance by using E=x-$$\mu$$ = 8.28-8.20 = .08
and n = (z _$$\alpha$$/2)$$\sigma$$/ E)^2 to get $$\sigma$$=.141. Then I plugged this into Z_0 = x-$$\mu$$/$$\sigma$$/$$\sqrt{n}$$. Then I found Z_0 to be 1.97 which would mean the mean 8.20 would be rejected, but I don't think this is right. Can someone tell me what I'm doing wrong and help me out?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution