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

If the life of the Tires ( in days ) follows normal distribution.

Assume that the population standard deviation( ) is known from the past data

Suppose the management want to estimate the population mean within the 50 days from the mean life of the Tiers with the 95% confidence .

That is E = 50 and c = confidence level = 95%

If the management want to estimate population mean by taking samples from the population and want to achieve the above objective then he/she need to select the appropriate sample size ( n )

Following formula help to find the size of sample.

Where Z_c is the critical value and for c =confidence level = 0.95

Z_c = 1.96

= assume that it is known from the past data ( take it as 500 days ) .  

E = 50 days

So that

Note that here we use hypothetical values to find the sample size n