The American Sugar Producers Association wants to estimate the meanyearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviationof 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?
This solution explains the best estimate of the population mean and the appropriate usage of the t-distribution. It also calculates the t value for a 90% confidence interval and the confidence interval for the population mean.