Question

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.

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 estimates a sample parameter.

B. The interpretation is incorrect. A confidence interval is not about a population parameter.

C. The interpretation is incorrect. A confidence interval is not about individuals in the population.

D. The interpretation is correct. A confidence interval estimates a population parameter.

b) 95% of the students paid between $1372 and $1562.

c) We're 95% sure that students in this sample averaged between $1372, $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 of all students pay between $1372 and $1562.

Answer 1

a) 95% of all students pay between​ $1372 and​ $1562 for food.

comment:

we are 95 % confident that the mean cost of food for one term is between 1372 and 1562

C. The interpretation is incorrect. A confidence interval is not about individuals in the population

b) 95% of the students paid between $1372 and $1562.

Incorrect, because the CI is about the population mean and thus not about individual students

c) We're 95% sure that students in this sample averaged between $1372, $1562 for food.

Incorrect

Because we know that the sample mean of this sample between 1372 and 1562. The sample mean is (1372_1562)/2 = 1467

d) 95% of all samples of students will have average food costs between $1372 and $1562

Incorrect

because the CI is about the population mean and not about sample means

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

correct

The given statement is nearly identical to interpretation of the CI at the top