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Math Help - Confidence interval. Need someone to check my answer

  1. #1
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    Confidence interval. Need someone to check my answer

    A machine is producing metal pieces that are cylindrical in shape. A sample of pieces is taken and the diameters are 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03. Find the 99% confidence interval for the mean diameter of pieces from this machine, assuming an approximate normal distribution

    My final answer varies from the answer given in the textbook. I'd like for someone to go over my work and point out my error. Please double check my mean and standard deviation as well.

    \bar{x}=1.005556

    \sigma=0.025442

    \alpha=0.01

    Z_{\frac{0.01}{2}}=2.575 Please double check this as well

    n=9

    pr(1.005556-(2.575(\frac{0.025442}{\sqrt{9}}<\mu <1.005556+(2.575(\frac{0.025442}{\sqrt{9}})=0.99

    pr(0.984482<\mu<1.026629)=0.99) Is the final answer that I get. However, the book has

    0.978<\mu<1.033Can someone please tell me where my error is? Thanks.
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  2. #2
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    Nevermind. I'm an idiot.  \sigma is unknown so I need to use the t-distribution
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