The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 27 kilograms (kg) with a standard deviation of 9 kg. Assume a normal population.
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% confidence interval, what is the value of t?
d. Develop the 90% confidence interval for the population mean.
e. Would it be reasonable to conclude that the population mean is 28 kg?