A clean air standard requires that vehicle exhaust emissions not exceed specifie

Question

A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Suppose state regulators double check a random sample of cars that a disreputable repair shop has certified as passing. They will revoke the shop’s license if they find significant evidence that the shop is certifying vehicles that do not meet the emissions standards. Consider the following hypotheses:

H0: It is not the case that the repair shop is certifying cars that fail the emissions standards. H1: The repair shop is certifying cars that fail the emissions 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?

d) Which type of error would environmentalists consider more serious?

e) Define “power” in the context of this problem.

f) Will the power be greater if the state regulators test 20 or 40 cars? Why?

g) Will the power be greater if they use a significance level of = 0.05 or = 0.10? 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

a)

The type-I error is rejecting Null hypothesis when it is true.

The repair shop is certifying cars that fail to meet the emission standards.

b)

The type-II error is rejecting Alternative hypothesis when it is true.

That is, the repair shop is certifying cars that do not fail to meet the emission standards.

c)

Type-I error should seriously taken by the shops owner.

d)

Type-I error

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