Question

Completely and thoroughly explain how the calculation of the Minimum Sample Size could be used by a company that makes Tires for automobiles, or trucks, or heavy-duty farm equipment, to help them to make good management decisions based on the collection of enough data to support those decisions.

Answer 1

To get a smaller margin of error a larger sample size is needed. So the minimum sample size to be used by the company for the studies that would help with management decisions would depend on how much Margin of error is desired in the results.

n >= (z*σ/MOE)²

is the formula for the minimum sample size to be used in a study. σ which is the population standard deviation and mostly unknown can be estimated by running a pilot test( a small study ahead of time) or standard deviation for a sample can be used ( risky though because sample might be too small).

A desired MOE would depend on the cost effectiveness of the study and that of the tires. Putting the variables in place along with z score for the Confidence Interval of the study minimum sample size can be obtained by rounding off the right hand side expression to the next integer.