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

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    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
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    Quote Originally Posted by land144 View Post
    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 ....
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    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.
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    Quote Originally Posted by land144 View Post
    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?
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    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
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    Quote Originally Posted by land144 View Post
    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.
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    isn't variance = sigma^2 / n and for this we have sigma=3 and n=20 so variance is 9/20 ?
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    Quote Originally Posted by land144 View Post
    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 [tex]\sigma = 3[/tex]). z-test it is.

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