Question

A USA Today article in 2008 said that Americans have visited 16 states. A sample of 50 students from a school revealed that they had visited an average of 9.48

states with a standard deviation of 7.13. The 95% confidence interval is (7.46, 11.50).

a) Which of the following interpretations, if any, are correct? Select all that apply.

A. With 95% confidence, the average number of states visited by those 50 people is between 7.46 and 11.50.

B. With 95% confidence, the average number of states visited by all students at the school is between 7.46 and 11.50.

C. Based on the 95% confidence interval, there is evidence that the average number of states all students at this school have visited is different than 16.

D. 95% of all the students at this school have visited between 7.46 and 11.50 states.

E. There’s a 95% chance that average number of states visited by all students at the school is between 7.46 and 11.50.

b) Explain what’s wrong with the incorrect interpretations above, if there are

any.

Answer 1

Solution:

a)

Given 95% confidence interval is ,

(7.46, 11.50)

Interpretation given in A,B,D and E are all correct. Only C is incorrect.

b) Wrong interpretation is, Based on the 95% confidence interval, there is evidence that the average number of states all students at this school have visited is different than 16. Because our area of interest is that 16 states where students are visited. So we talk about 16 states not different than that. Hence this option is wrong

Done