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.

e)In this context, what is meant by the power of the test the regulators are conducting?

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 is only a little out of compliance or a lot? Why?

Explanation / Answer

e) here power of the test is probability of rightly revoking  the shop’s license if they certifying vehicles that do not meet standards

f)as for higher sample size variablilty is less and therefore easy to detect a difference ; hence power be greater if they test 40 cars

g)as with increased level of significance ; probability of revoke the shop’s license will increase for low critical values; hence power will increase for 10% level of significance

h) power will be less when only a little out of compliance or a lot ; cause it is difficult to detect differnence between a shop whcih meets the compliance and which do not.

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