# Use of Confidence Intervals and Sample Size Determination

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.

https://brainmass.com/statistics/sample-size-determination/confidence-intervals-sample-size-determination-375038

#### Solution Preview

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

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 = ...

#### Solution Summary

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