Answer:
e) We're 95% sure that the average amount all students pay is between $1372 and $1562.
Explanation:
A x% confidence interval of a sample being (a,b) means that we are x% sure that the true mean of the population is between a and b.
In this problem, we have that:
95% confidence interval for the mean cost of food for one term (of three in the Dartmouth trimester calendar) is ($1372, $1562).
a) 95% of all students pay between $1372 and $1562 for food.
We are 95% sure that the true mean value of the mean paid by all students is between $1372 and $1562. This is not correct.
b) 95% of the sampled students paid between $1372 and $1562.
We use the sample to find the confidence interval for the population. So this is not correct.
c) We're 95% sure that students in this sample averaged between $1372 and $1562 for food.
Not in this sample, but in all the population of students.
d) 95% of all samples of students will have average food costs between $1372 and $1562.
We are 95% sure that the true mean value of the mean paid by all students, that is, the population, is between $1372 and $1562. This is not correct.
e) We're 95% sure that the average amount all students pay is between $1372 and $1562.
This is the correct answer