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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:
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 = ...

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