A clean air standard requires that vehicles exhaust emissions not exceed specifi

Question

A clean air standard requires that vehicles exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double check a random sample of cars that a suspect repair shop has certified as okay. They will revoke the shop’s license if they find significant evidence that the shop is certifying vehicles that do not meet standards. a) In this context, what is a Type I error? b) In this context, what is a Type II error? c) Which type of error would the shop’s owner consider more serious? Explain. d) Which type of error might environmentalists consider more serious? Explain. e) In this context, what is meant by the power of the test the regulators are conduction? f) Will the power be greater if they test 20 or 40 cars? Why? g) Will the power be greater if they use a 5% or a 10% level of significance? Why? h) Will the power be greater if the repair shop’s inspectors are only a little out of compliance or a lot? Why?

Explanation / Answer

Solution:

a) The null is that the shop meets the standards, the alternate is that the shop doesn’t meet the standards.
b) It is decided that the shop is not meeting standards when it is.
c) Thje shop is certified as meeting standards when it is not.
d) Type II
e) The probability of detecting the shop is not meeting standards when it is not.
f) 40 cars, larger n.
g) 10%. More chance to reject H0.
h) A lot. Larger differences are easier to detect.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.