SOLUTION: 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 stand
Algebra.Com
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
----------------
What is the best estimate of this value? The mean of the same is your best est.
----------------
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.
----------------
What assumption do you need to make?
The amount of sugar consumed by people is normally distributed.
----------------
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
---------------------
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
---------------------
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.
===================
Cheers,
Stan H.
RELATED QUESTIONS
The American Sugar Producers Association wants to estimate the mean yearly sugar... (answered by stanbon)
The sugar producers association wants to estimate the mean yearly sugar consumption. A... (answered by Boreal)
The American Sugar Producers Association wants to estimate the mean yearly sugar... (answered by JBarnum)
The U.S. Dairy Industry wants to estimate the mean yearly milk
consumption. A sample... (answered by coursehelpcj)
The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of... (answered by stanbon)
How much sugar is in a cookie with reduced sugar?
A random sample of 20 reduced-sugar... (answered by stanbon)
Perry wants to make 10 gal. of a 58% sugar
solution by mixing together a 70% sugar... (answered by lwsshak3)
The operations manager of a sugar mill in Chesterville wants to estimate the average size (answered by Boreal)
The price of sugar increases by 32%.a family reduce its consumption so that the... (answered by Theo)