After surveying students at a​ college, a campus organization calculated that a​ 95% confidence interval for the mean cost of food for one term is​ ($1372, $1562). Now the organization is trying to write its report and is considering the following interpretations. Comment on each. Complete parts a through e below.       Question content area bottom Part 1 ​a) 95% of all students pay between​ $1372 and​ $1562 for food.   Comment on the given interpretation. Choose the correct answer below.     A. The interpretation is incorrect. A confidence interval is not about individuals in the population.   B. The interpretation is incorrect. A confidence interval estimates a sample parameter.   C. The interpretation is correct. A confidence interval estimates a population parameter.   D. The interpretation is incorrect. A confidence interval is not about a population parameter. Part 2 ​b) 95% of the sampled students paid between​ $1372 and​ $1562.   Comment on the given interpretation. Choose the correct answer below.     A. The interpretation is incorrect. A confidence interval is not about individuals in the sample.   B. The interpretation is incorrect. A confidence interval is not about a population parameter.   C. The interpretation is incorrect. One knows that all of the sampled students paid between​ $1372 and​ $1562.   D. The interpretation is correct. A confidence interval estimates a sample parameter. Part 3 ​c) One is​ 95% sure that students in this sample averaged between​ $1372 and​ $1562 for food.   Comment on the given interpretation. Choose the correct answer below.     A. The interpretation is incorrect. A confidence interval estimates the standard deviation of a population.   B. The interpretation is correct. A confidence interval estimates a sample parameter.   C. The interpretation is incorrect. A confidence interval estimates a sample parameter.   D. The interpretation is incorrect. The mean cost for students in the sample is known to be​ $1467. Part 4 ​d) 95% of all samples of students will have average food costs between​ $1372 and​ $1562.   Comment on the given interpretation. Choose the correct answer below.     A. The interpretation is incorrect. One knows that all samples will have average food costs between​ $1372 and​ $1562.   B. The interpretation is incorrect.​ 95% of all samples will have average food costs within two standard deviations of the true population mean.   C. The interpretation is incorrect. A confidence interval estimates a sample parameter.   D. The interpretation is correct. A confidence interval estimates a population parameter. Part 5 ​e) One is​ 95% sure that the average amount all students pay is between​ $1372 and​ $1562.   Comment on the given interpretation. Choose the correct answer below.     A. The interpretation is correct. A confidence interval estimates a population parameter.   B. The interpretation is incorrect. A confidence interval estimates a sample parameter.   C. The interpretation is incorrect. A confidence interval estimates individual​ values, not sample parameters.   D. The interpretation is incorrect. A confidence interval is not about individual students in the population.

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After surveying students at a​ college, a campus organization calculated that a​ 95% confidence interval for the mean cost of food for one term is​ ($1372, $1562). Now the organization is trying to write its report and is considering the following interpretations. Comment on each. Complete parts a through e below.
 
 
 

Question content area bottom

Part 1
​a) 95% of all students pay between​ $1372 and​ $1562 for food.
 
Comment on the given interpretation. Choose the correct answer below.
 
 
A.
The interpretation is incorrect. A confidence interval is not about individuals in the population.
 
B.
The interpretation is incorrect. A confidence interval estimates a sample parameter.
 
C.
The interpretation is correct. A confidence interval estimates a population parameter.
 
D.
The interpretation is incorrect. A confidence interval is not about a population parameter.
Part 2
​b) 95% of the sampled students paid between​ $1372 and​ $1562.
 
Comment on the given interpretation. Choose the correct answer below.
 
 
A.
The interpretation is incorrect. A confidence interval is not about individuals in the sample.
 
B.
The interpretation is incorrect. A confidence interval is not about a population parameter.
 
C.
The interpretation is incorrect. One knows that all of the sampled students paid between​ $1372 and​ $1562.
 
D.
The interpretation is correct. A confidence interval estimates a sample parameter.
Part 3
​c) One is​ 95% sure that students in this sample averaged between​ $1372 and​ $1562 for food.
 
Comment on the given interpretation. Choose the correct answer below.
 
 
A.
The interpretation is incorrect. A confidence interval estimates the standard deviation of a population.
 
B.
The interpretation is correct. A confidence interval estimates a sample parameter.
 
C.
The interpretation is incorrect. A confidence interval estimates a sample parameter.
 
D.
The interpretation is incorrect. The mean cost for students in the sample is known to be​ $1467.
Part 4
​d) 95% of all samples of students will have average food costs between​ $1372 and​ $1562.
 
Comment on the given interpretation. Choose the correct answer below.
 
 
A.
The interpretation is incorrect. One knows that all samples will have average food costs between​ $1372 and​ $1562.
 
B.
The interpretation is incorrect.​ 95% of all samples will have average food costs within two standard deviations of the true population mean.
 
C.
The interpretation is incorrect. A confidence interval estimates a sample parameter.
 
D.
The interpretation is correct. A confidence interval estimates a population parameter.
Part 5
​e) One is​ 95% sure that the average amount all students pay is between​ $1372 and​ $1562.
 
Comment on the given interpretation. Choose the correct answer below.
 
 
A.
The interpretation is correct. A confidence interval estimates a population parameter.
 
B.
The interpretation is incorrect. A confidence interval estimates a sample parameter.
 
C.
The interpretation is incorrect. A confidence interval estimates individual​ values, not sample parameters.
 
D.
The interpretation is incorrect. A confidence interval is not about individual students in the population.
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