S2 help, think book may be wrong.

Good evening all. I'm revising for my stats exam and I've come across a question which I think may have been wrote wrong. It's Normal Distribution stuff.

Question:
A machine set to produce metal discs of diameter 11.90cm has an annual service. After the service, a random sample of 36 discs is measured and found to have a mean diameter of 11.930 cm and gives an estimated population variance of 0.072 cm^2. Test, at the 1% significance level, whether the machine is now producing discs of mean diameter greater than 11.90 cm.

For reference, 1% is 2.326 sds away from the mean.

Thanks :smile:

Reply 1

Totally Tom

Errrr, what do you get?

We're not going to blindly do it for you.

Been a while since I've done this, You set H0 and H1 where H0 is there is no change and H1 is the mean is greater than 11.930

So then you do (O-E)/v And if this is in the critical area you reject H0 and accept H1 but if not you accept H0 and reject H1?

Reply 2

Shadow!

Hah sure, sorry about that.

Well when I use the variance as 0.072 i get:

(11.930-11.9)/√(0.072/36) = 0.6708

And 1% range being 2.326, shows that it isn't. However book says 2.5, which leads me to believe that 0.072 is not the variance, but the standard deviation.
As from our equation above:

(11.930-11.9)/(0.072/√36) = 2.5

What do you reckon?