Stat1005 (1 Viewer)

[tennille]

Okie, I've been doing some practice questions from the Primer of Statistics book (I've done some exam questions, but there aren't any answers for them), mainly for the statistical tests (Chapter 3 Review Problems).

Q15) A batch of concrete was made to the specification that the mean compression strength (the rpessure at breaking point withstood by a uniform test cylinder) should be at least 200 units. The compression strengths of 10 randomly chosen specimens were:

196, 199, 204, 198, 205, 210, 185, 197, 184, 194

Records show that the standard deviation of compression strength is 12 units and the strengths seem to follow a normal model. Construct and apply a one-sided test of significance.

So I wrote that H0: p = 200 and H1: p > 200

After all the working out using the one-sided normal test, I end up with a p-value of:

P (z > -0.74), which is equivalent to P (z < 0.74)
= 0.7703

So the data supports H0.

But the answer at the back of the book states that the p-value is 0.23 (ie 1-0.7703) and that there is not sufficient evidence for us to believe that the batch has a mean compression strength below 200.

It looks like they tried to prove p < 200. Is that true, I did I miss out on something?

Thanks.

 

[acmilan]

When it says should be at least 200, i think it means H1 is mu < 200

My reasoning: H0 is true when nothing goes wrong, if nothing goes wrong, average is at least 200. So if H0 is true then that condition is satisfied since mu = 200 means average is at least 200. H1 is what is happening if theres something going wrong. Something goes wrong when the 'at least 200' condition is false, so H1 is mu < 200.

That's the way i see it, could be wrong.

 

[stazi]

acmilan is correct (brings back econometric memories )

a lot of these can be confusing and amibuous though. thats why i hated hypothesis tests.

 

[tennille]

Thanks guys.