Solve the EAI Problem
EAI has 2500 managers given the information provided. This is also the population size (n) used for the calculations made. Next, I found the salary mean of the population size using the AVERAGE function in Excel which calculated the mean to be $51,800.00. After this was found, I used the same annual salary numbers and plugged them into the STDEV.S function to find the standard deviation of 4000.000067. I then found the number of managers that took the company’s management training program, which was 1500, and used that divided by the sample size to find that the proportion (P) who completed the course was 0.6. In order to establish a random sample of 50 managers, I had to use the function in Excel called RAND which assigned a random number to each manager. Because these numbers calculated by the RAND function are constantly changing, I had to copy and paste the values returned from that function and move them to the next column in order to avoid getting different results every time I moved to a different section in the Excel document. I was then able to filter the RAND column from largest to smallest in order to select my random sample of 50 managers.
The new sample size (n) became 50 and the same calculations were used to find the mean of $52,654.88, the standard deviation of 3928.48, and the proportion (p-bar) of 0.64 representing the managers that took the company’s management training program. From the sample selected, 32 of the 50 managers participated in this program. So, this provides information showing that 64% of managers have taken the management training program. Based on the sample information, the point estimator is 52,654.88, which is also x-bar. The value of x-bar is important because it is used to make inferences about the population mean. Since the standard deviation is 3928.48 that means anything between 48,726.40 and 56,583.36 is within one standard deviation of the mean. Approximately 68% of the managers should be within this range.
