Question 136446: 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 is 63 pounds?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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? 60 lbs
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What is the best estimate of this value? The mean of the same is your best est.
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b. Explain why we need to use the t distribution.
You are estimating the population mean.
Comment: Every text differs on the reasoning for this. Check your text.
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What assumption do you need to make?
The amount of sugar consumed by people is normally distributed.
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c. For a 90% confidence interval, what is the value of t?
That depends on the degrees of freedom for the problem.
In your problem df=15, so the t-value is 1.753
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d. Develop the 90% confidence interval for the population mean.
x-bar = 60
E = 1.753 = 8.765
90% CI: (60-8.765 < u < 60+8.765) = 51.235 < u < 68.765
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e. Would it be reasonable to conclude that the population mean is 63 pounds?
At this point all you could say is that the value is in the 90% CI.
You cannot claim that you have 90% confidence that the mean is 63 lbs.
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Cheers,
Stan H.
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