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Math Help - Confidence Intervals and Sample Size

  1. #1
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    Smile Confidence Intervals and Sample Size

    What is the 2 sided confidence interval for the mean strength of a new structural column? The sample size is 25, the mean is 15,000 pounds, and the sample standard deviation is 200 lbs. Use a confidence level of 95 %.
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  2. #2
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    Quote Originally Posted by ccdelia7 View Post
    What is the 2 sided confidence interval for the mean strength of a new structural column? The sample size is 25, the mean is 15,000 pounds, and the sample standard deviation is 200 lbs. Use a confidence level of 95 %.
    This is a simple substitution into a standard formula that should be in your textbook or class notes. The formula is here too: 1.3.5.2. Confidence Limits for the Mean.

    Where exactly are you stuck?
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    Honestly, I just think my professor is not clear...I am trying to study for a final, and I cannot figure this problem out. This was an old homework problem, and I don't know how to start. Can you walk me through it?
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    I believe, from this data, beta is .05?
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    Quote Originally Posted by ccdelia7 View Post
    Honestly, I just think my professor is not clear...I am trying to study for a final, and I cannot figure this problem out. This was an old homework problem, and I don't know how to start. Can you walk me through it?
    The formula in the link I gave you is \overline{Y} \pm t_{\alpha/2, \, N-1} \frac{s}{\sqrt{N}}.

    Substitute \overline{Y} = 15,000, s = 200 and N = 25.

    \alpha = 0.05 and N = 25 mean that you require the value of t_{\alpha/2, \, N-1} = t_{0.025, \, 24} (24 is the number of degrees of freedom). From a standard table of critical values I get t_{0.025, \, 24} = 2.064.

    Substitute all this into the formula to get your confidence interval.
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  6. #6
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    Please correct me if I'm wrong...

    Lower limit = 14983.5
    Upper limit = 15016.5

    I substituted what you told me. That's my problem, I dont know where to start on a problem, because there are so many different tests...
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  7. #7
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    I'm sorry, forgot the square root...

    Lower Limit = 14917.6
    Upper Limit = 15082.6
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  8. #8
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    Quote Originally Posted by ccdelia7 View Post
    I'm sorry, forgot the square root...

    Lower Limit = 14917.6 Mr F says: I get 14917.44
    Upper Limit = 15082.6
    I'd be inclined to round to 14917 lbs and 15083 lbs.
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