Question

In the Star and Tribune newspaper, there is an article entitled “1 in 8 school buses fail tests.”   The article says that the overall statewide proportion of school buses that fail safety tests is 9%. However, one bus company has a higher rate of over 12%. Assume that we want a new estimate for the statewide proportion of school buses that fail the safety inspection. We take a sample of 200 buses and find that 20 buses fail the safety inspection.

a.) What is the sample proportion of buses that fail the test?

b.) If we construct a 99% confidence interval estimate for the true proportion of all Minnesota school buses that fail the safety tests, what is the lower limit of the interval?

c.) If we construct a 99% confidence interval estimate for the true proportion of all Minnesota school buses that fail the safety tests, what is the upper limit of the interval?

d.) This question assumes that you have constructed a 99% confidence interval estimate for the true proportion of all Minnesota school buses that fail the safety tests. Write a sentence or two that describes or interprets the confidence interval that you constructed.  

e.) How large a sample would you have to take in order to construct a 95% confidence interval estimate and achieve a margin of error of plus or minus 2%?

Answer 1