After surveying students at dartmouth college, a campus organization calculated that a 95% confidence interval for the mean cost of food for one term (of three in the dartmouth trimester calendar) is ($1372, $1562). now the organization is trying to write its report and is considering the following interpretations. comment on each. a) 95% of all students pay between $1372 and $1562 for food. b) 95% of the sampled students paid between $1372 and $1562. c) we're 95% sure that students in this sample averaged between $1372 and $1562 for food. d) 95% of all samples of students will have average food costs between $1372 and $1562. e) we're 95% sure that the average amount all students pay is between $1372 and $1562.

e) We're 95% sure that the average amount all students pay is between $1372 and $1562.

Step-by-step 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