The American Sugar Producers Association wants to estimate the mean yearly sugar
ID: 2959073 • Letter: T
Question
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% 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 would be 63 pounds?
Explanation / Answer
Answer (a):
The sample mean is an unbiased estimator for the population mean, so we can guess that the best estimate is 60 pounds.
Answer (b):
We have to use the t distribution since we have a very small sample size (under 30 or so). We also have to assume that the data is normally distributed.
Answer (c):
We have to use a t table We set df = sample size - 1 = 16 - 1 = 15. We look in the 0.10 column for the 90% interval. t = 1.7531
Answer (d):
The interval goes from:
mean - t*stdev/sqrt(N) to mean + t*stdev/sqrt(N)
60 - 1.7531*20/sqrt(16) to 60 + 1.7531*20/sqrt(16)
51.2345 to 68.7655
Answer (e):
Yes because 63 pounds is among the confidence intervals.
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