Mba 510 Problem Set Two
Chapter 9
Exercise 12: The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds.
a. What is the value of the population mean? What is the best estimate of this value?
b. Explain why we need to use the t distribution. What assumption do you need to make?
c. For a 90 percent confidence interval, what is the value of t?
d. Develop the 90 percent confidence interval for the population mean.
e. Would it be reasonable to conclude that the population mean is 63 pounds?
Answer:
a. Population mean will be difficult to determine as the data is only from a sample of the population. However, the best estimate will be the mean of the studied sample i.e. 60 pounds.
b. The use of the t distribution is important as the standard deviation is unknown and the sample size is small. We do not know the exact population size and only a small sample has been studied. However, we can assume that the population is normally distributed.
c. Value of t in the above case is 1.753
d. For Sample mean of 60 pounds and with 20 being the standard deviation the confidence interval at 90% at lower is 51.235 and upper is 68.765.
e. It would be reasonable to say that the population mean can be 63 as it falls between the confidence interval values of upper and lower with a confidence interval of 90%. Leaving 10% probability of the value falling outside the upper and lower value.
The reason behind choosing this question is because I can relate my current job setup the above computation. We deal with insurance companies and patients on daily basis in reference to their health care bills, claims and payments. Understanding how a confidence interval is computed can help in determining levels of payment patterns, copayment levels, and insurance coverage...
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