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    Use of Confidence Intervals and Sample Size Determination

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    The Modulus of rupture (MOR) for a particular grade of pencil lead is known to have a standard deviation of 250 psi.

    a. A random sample of 16 pencil leads yielded a sample mean of 6490. Construct a 90% confidence interval for the true mean MOR.
    b. Find the sample size required to estimate the true mean MOR to within ± 100 using a 90% confidence interval.
    c. What did you assume to do these analyses? How can you check these assumptions.

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    Solution Preview

    step-by-step explanation and solution is provided in the attachment.

    Part (a)
    Here we have
    Sample Mean ( )= 6490
    Standard Deviation (σ)= 250
    Here we have n = 16
    We will use standard normal distribution because the population standard deviation is known.
    Z = ...

    Solution Summary

    The solution of each part is provided step wise so that it can be easy to understand.