# Hypothesis Testing

• Apr 6th 2008, 02:04 PM
Thatgirl
Hypothesis Testing
Hello,
I am looking for any help in clarifying if I am on the right track, or help to put me on the right track. There is only 1 question with my answers for now, and I would really appreciate any input.

Also for the question I have:
-stated the null and alternative hypothesis
-stated the critical region to reject or fail to reject the null
-Identified the test stat
-found the test stat
-stated the conclusion.

The question:

A customer is in need of a large supply of copper tubing that is cut 1.25 meters long. A plumbing supply company guarantees that if you order a specified lenght, you will receive what you ordered within a standard deviation=0.0001. To test the companies guarantee, a sample of 10 pieces of the tubing was taken. The mean length of the tubing was 1.2502 meters. Assume the population is normally distributed.
a)Is there a significant difference in the specified length of the tubing at the 0.01 significance level? Based on your answer, should the customer trust the guarantee?
b)Calculate the p-value at the 0.01 significance level. Is it significant?

Ho: u=1.25 H1: u=/=1.25
Critical region: Fail to reject Ho if the test statistic falls between 2.33 and -2.33. Reject Ho if the test statistic does not fall between 2.33 and -2.33.
z=6.3 with test stat=0.0001
Conclusion: There is not sufficient sample evidence to warrant rejection of the claim that if you order a specified length of pipe, you will receive it within a standard deviation of 0.0001.
a)No, there is not a significant difference in the length of tubing at the 0.01 significance level. The customer should trust the company's guarantee.
b) P-value=0.0002 and it is not significant.
• Apr 6th 2008, 02:51 PM
bobak
So you have $\displaystyle X \sim N ( 1.25 , 0.0001 )$

Now I could be wrong here, but the manufactures claim is based on the accuracy of their cut. How I see if their cut is not so accurate you will get a variety of tubes shorter and longer than the required length so the average will always be pretty much the same. I reckon that you should have $\displaystyle H_0 : \sigma = 0.0001 \ \ \ \ H_1 : \sigma > 0.0001$.

So want you want is to find c $\displaystyle P ( X < c \ \cap X > 2\mu - c \ | \ X \sim N ( 1.25 , 0.0001 ) = 0.01$ note his is a two tailed test.

use to symmetry of the distribution. to get.

$\displaystyle 2 P ( X > 2\mu - c ) = 0.01$

then you transform to Z
$\displaystyle P ( Z > \frac{\mu - c}{\sigma} ) = 0.005$

$\displaystyle P ( Z < \frac{\mu - c}{\sigma} ) = 0.995$

using tables I get

$\displaystyle \frac{\mu - c}{\sigma} = 2.6$

I'll put some values in now
$\displaystyle \frac{1.25 - c}{0.0001} = 2.6$

giving [Math] c = 1.24974[/tex]
and [Math] 2 \mu - c = 1.25026[/tex]

so if the manufactures claim is true, 99% of the time we should get $\displaystyle 1.24974 < \mu < 1.25026$

1.2502 is within the range (only just) so we can trust their claim.
• Apr 6th 2008, 03:12 PM
Thatgirl

I thought however, that if > was used, its a right tailed test.

Its all so confusing. And what is the c represent?
• Apr 6th 2008, 03:20 PM
bobak
Quote:

Originally Posted by Thatgirl