The operations manager from question above (in the link above) wants to make sure the right sample size...

The operations manager from question above (in the link above) wants to make sure the right sample size was used to collect the observations and calculate the standard time.
The company’s owner will be satisfied within an accuracy 2% in the time estimates but wants to be 99% confident.

Determine of the sample size of 10 that was used was sufficient to meet the owner’s expectations. Describe your findings. It helps to remember to recall how to calculate the standard deviation from the observations in the question above.

Below is information to help:

Expert Answers
pohnpei397 eNotes educator| Certified Educator

In order to determine whether the sample size was large enough, we need to do some basic statistics.  The formula for finding the proper sample size is:

desired sample size =  (zs/h(xbar))^2

Here is a list of what each of the variables in the equations is:

  • h = the level of accuracy we are willing to accept
  • s = the standard deviation of the initial observation
  • z = the number of standard deviations required for our desired confidence level of 99%.
  • xbar = the average of the initial observations that were conducted in the question

From your question, we know that

  • h = 2% or .02
  • z = 2.58 (this is a known quantity as 99% confidence is a common confidence level.  Follow this link to see how it is calculated.)
  • xbar = 7.176 (found in the answer to the question that you linked to)

Now, we see that we have to find the standard deviation in order to have all of the information that we need.  To find the standard deviation, we need to take the following steps:

  • Find the mean of the observed times (7.176 minutes). 
  • Subtract the mean from each actual time observed. 
  • Square each difference and add the squares.
  • Divide the sum of the squares by the number of observations minus 1
  • Find the square root of this number.  The square root is the standard deviation.

If we go through all of these steps using the data from your previous question, we find that the standard deviation for this data set is .17.

Now we can find the desired sample size:

desired sample size =  (zs/h(xbar))^2

= (2.58*.17/.02(7.176))^2

= (.439/.143)^2

= 3.07^2

= 9.42

What this tells us is that 9.42 observations would have been sufficient.  Since we actually did 10 observations, the number was sufficient.