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Determining sample size needed to test hypothesis

  1. Mar 24, 2006 #1
    This is a statistics and probability question.
    I've been trying to figure this out for hours but I'm getting nowhere:
    I have to test the hypothesis that the true average value of a sample is 6.2. I will reject the null hypothesis if with 95% confidence if the true average value is indeed 6.2 or reject the null hypothesis if the true average is 6.0.

    I need to calculate the number of samples needed to test the hypothesis with the required accuracy, as well as the cut-off level, assuming a standard deviation of 0.4.

    I have never done a problem where average value or sample size wasn't given, any help on how to get started would be greatly appreciated
     
  2. jcsd
  3. Mar 24, 2006 #2
    Can you type in the exact problem? I think I can help you on this, but I need to know the problem word for word first :).

    Usually, you are given the margin of error for these kinds of problems...
     
    Last edited: Mar 24, 2006
  4. Mar 24, 2006 #3
    sure,
    An engineer wants to test the hypothesis that the true average voltage threshold V of a diode is 6.2 Volts as labeled.

    He will accept the null hypothesis with 95% confidence if the true average voltage is indeed 6.2 Volts, and will reject the null hypothesis with 95% confidence if the true average voltage is instead 6.0 Volts

    calculate the number of diodes that he will need to measure and the cut-off level for the voltage in order to test the hypothesis with the required accuracy. Assume the standard deviation of the diodes is 0.4V

    Thanks in advance, appreciate your help
     
  5. Mar 24, 2006 #4
    Thank you :-)

    Okay, if you were to write out a 95% confidence interval for this, how would you write it?

    6.2 +- ??

    Think about it. If you reject H0 at 6.0, what value do you think goes in where the question marks are?
     
    Last edited: Mar 24, 2006
  6. Mar 24, 2006 #5
    ah ok, that would be 0.2, which is the margin of error right? then i can solve the equation for the sampe size...I got a value of 11 using a one tailed test. does that sound right to you, or do you think this is a two tailed.

    Many thanks :)

    by the way, im still not sure how i would find the cutoff value, any ideas on that?
     
  7. Mar 24, 2006 #6
    It sounds one-sided, although it doesn't really say. Regardless, I don't think your answer is correct. I think you derived the correct equation, but I think you used the z* value of 1.645 (90% confidence) instead of 1.960 (95% confidence). Perhaps my memory has failed me...
     
  8. Mar 24, 2006 #7
    Actually, according to my handy table here, 1.645 is for a 95% one-sided confidence; 1.96 is used for two sided 95% confidence (corresponds to 97.5%). Anyways, thanks a lot, I can't believe I spent so much time on that lol. As for the cutoff level , what do you think they mean by that? I would guess 6.0 but that seems too easy...
     
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