Download The American Sugar Producers Association wants to estimate the

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?
(a) Population mean is equal to sample mean, which is 60 pounds.
The best estimate is 60 pounds because sample mean is itself an unbiased estimator of the population
mean.
(b) Here, n < 30. Therefore we need to use the t- distribution. We need to assume that the mean yearly
sugar consumption among the population is normally distributed.
(c) Dof = 16 – 1 = 15 and t[15, (1-0.9)/2] = 1.753 [From Tables]
(d) The 90% confidence interval for the population mean is
[(60 - 1.753 * 20/16, 60 + 1.753 * 20/16] = (51.235 pounds, 68.765 pounds)
(e) Yes, we may conclude that the population mean is 63 pounds since 63 lies within the above interval.