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Using approximations to the binomial distribution

  1. Jan 9, 2015 #1
    1. The problem statement, all variables and given/known data
    This is the problem I am given. pic1.jpg . It is in he picture below or in the thumbnail. I was also told that since ##n## is big enough that I can use normal approximations.

    2. Relevant equations


    3. The attempt at a solution
    I think that ##C_{\alpha}=C_{0.1}=2.33## which I got off the Z-score chart. The test statistic given looks like the one given for a binomial distribution given by where ##Z=\dfrac{x-np}{\sqrt{npq}}=\dfrac{\frac{x}{n}-p}{\frac{\sqrt{pq}}{\sqrt{n}}}##. I am not sure if this right or not. But it seems like this is the only way of finding the critical value. Thanks
     
    Last edited: Jan 9, 2015
  2. jcsd
  3. Jan 9, 2015 #2

    RUber

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    I think you looked up the value for alpha = .01, you were asked for .1. If you are using a normal approximation, then this is all you need to find the critical value. Be sure to clarify if this is a one-tailed or two-tailed test. From the question T>C_alpha indicates you are checking to see if a majority are in favor--i.e. one-tailed, your process is correct. If you were just checking whether or not the null hypothesis held, you would use a two-tailed test. In that case, you would need to divide alpha by two.
     
  4. Jan 9, 2015 #3
    I see it is two tailed so I would use ##C=1.645## which would be my critical value.
     
  5. Jan 9, 2015 #4

    RUber

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    Right--In this case the two tailed test is for p = 50%, if you reject that, then you know it is either more or less. If you were only concerned with the proportion being more, then you could use a smaller critical value to get the same level of confidence.
     
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