# Math Help - How do you find a critical value when using a 1% significance level

1. ## How do you find a critical value when using a 1% significance level

The data i'm working with is
Sample mean(voltage)=128.25
variance=9/20
sample size=20
SD=3
Z=-2.61

The first part of what I was doing was a hypothesis test that the true voltage is 130 compared to the alternative less than 130. Which I worked out the Z score to be -2.61

What I have to do now is calculate the critical value for this test using a 1% significance level.. I know the answer is 128.44 but for the life of me I can't work out any formulas that will help me... can anyone shed some light??? Thanks

2. Originally Posted by land144
The data i'm working with is
Sample mean(voltage)=128.25
variance=9/20
sample size=20
SD=3
Z=-2.61

The first part of what I was doing was a hypothesis test that the true voltage is 130 compared to the alternative less than 130. Which I worked out the Z score to be -2.61

What I have to do now is calculate the critical value for this test using a 1% significance level.. I know the answer is 128.44 but for the life of me I can't work out any formulas that will help me... can anyone shed some light??? Thanks
What's 128.44 meant to be the answer to?? It's certainly not the critical value of z .....!!

You want the critical value of z at the 0.01 significance level for a one sided test.

To get it you look it up in a table of critical values! I get $z_{0.01} = -2.33$ ....

3. I'm not sure, the back of the book just says "Critical Value=128.44"

I assumed it had something to do with the fact that (I think) it's a left-handed hypothesis test (one tailed) or something like that... but I still can't work it out.

4. Originally Posted by land144
The data i'm working with is
Sample mean(voltage)=128.25
variance=9/20
sample size=20
SD=3
Z=-2.61

The first part of what I was doing was a hypothesis test that the true voltage is 130 compared to the alternative less than 130. Which I worked out the Z score to be -2.61

What I have to do now is calculate the critical value for this test using a 1% significance level.. I know the answer is 128.44 but for the life of me I can't work out any formulas that will help me... can anyone shed some light??? Thanks
Is SD = 3 the sample standard deviation or the population standard deviation? If the latter then you probably should be using a t-test, not a z-test.

Regarding the given critical value of 128.44 .... it almost looks like part of a confidence interval .... Were you asked to calculate a confidence interval?

5. Yeah It's a weird question. The data I'm given is sample standard deviation and it is a normal distribution. The entire quesiton says The Output voltage of a circuit is specified to be 130. A sample of 20 independent readings gave the mean reading as 128.25. Assume normal distribution with $\sigma$=3

So the quesiton says test the hypothesis that the true output voltage is 130 against the alternative it is less than 130, and I used a fomula that I thought was Z=128.25-130/(3/(sqrt(20)) and ended up with -2.61 (which is the correct answer)

So the part I'm stuck on is, What is t he critical value for the test in the part above using a 1% significance level.

I thought it might be a confidence interval but I couldn't figure it out? The answer just says "Critical Value = =128.44

6. Originally Posted by land144
Yeah It's a weird question. The data I'm given is sample standard deviation and it is a normal distribution. The entire quesiton says The Output voltage of a circuit is specified to be 130. A sample of 20 independent readings gave the mean reading as 128.25. Assume normal distribution with $\sigma$=3

So the quesiton says test the hypothesis that the true output voltage is 130 against the alternative it is less than 130, and I used a fomula that I thought was Z=128.25-130/(3/(sqrt(20)) and ended up with -2.61 (which is the correct answer)

So the part I'm stuck on is, What is t he critical value for the test in the part above using a 1% significance level.

I thought it might be a confidence interval but I couldn't figure it out? The answer just says "Critical Value = =128.44
1. The given answer is wrong.
2. You should be using a t-test since the population is normal but it's variance is unknown.

7. isn't variance = sigma^2 / n and for this we have sigma=3 and n=20 so variance is 9/20 ?

8. Originally Posted by land144
isn't variance = sigma^2 / n and for this we have sigma=3 and n=20 so variance is 9/20 ?
OK. My mistake. I didn't see the " $\sigma$=3" bit (by the way, these are the wrong tags for latex in this forum. It's $$\sigma = 3$$). z-test it is.

As stated earlier, the critical value is $z_{0.01} = -2.33$.

9. Thanks!!