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. Many states require that cars be tested annually to be sure they meet these standards. State regulators are checking up on repair shops to see if they are certifying vehicles that do not meet pollution standards.

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

b) Will the power be greater if they test 20 or 40 cars? Why?

c) Will the power be greater if they use a 5% or a 10% level of significance? Why?

d) Will the power be greater if the repair shop's inspectors are only a little out of compliance or a lot? Why?

a) In this context, what is meant by the power of the test the regulators are conducting? A. The power of the test is the probability of detecting a car that meets standards. B. The power of the test is the probability of detecting a shop that is meeting standards. C. The power of the test is the probability of detecting a car that does not meet standards. D. The power of the test is the probability of detecting a shop that is not meeting standards.

b) Will the power be greater if they test 20 or 40 cars? Why? A. The number of cars tested will not affect the power of the test B. Testing 20 cars will result in a greater power, because n is smaller. C. Testing 40 cars will result in a greater power, because n is larger.

c) Will the power be greater if they use a 5% or a 10% level of significance? Why? A. The power will be greater if a 10% level of significance, because there is a greater chance of rejecting Upper H 0H0. B. The power will be greater if a 5% level of significance, because there is a less chance of rejecting Upper H 0H0. C. The power will be greater if a 5% level of significance, because there is a greater chance of rejecting Upper H 0H0. D. The power will be greater if a 10% level of significance, because there is a less chance of rejecting Upper H 0H0.

d) Will the power be greater if the repair shop's inspectors are only a little out of compliance or a lot? Why? A. The power will be the same regardless of the level of compliance. B. The power will be greater if the repair shop's inspectors are out of compliance by a lot because larger differences are easier to detect. C. The power will be greater if the repair shop's inspectors are only a little out of compliance because smaller differences are more significant.

Explanation / Answer

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

C. The power of the test is the probability of detecting a car that does not meet standards.

b) Will the power be greater if they test 20 or 40 cars? Why?

A. The number of cars tested will not affect the power of the test.

c) Will the power be greater if they use a 5% or a 10% level of significance? Why ?

C. The power will be greater if a 5% level of significance, because there is a greater chance of rejecting Upper H0.

d) Will the power be greater if the repair shop's inspectors are only a little out of compliance or a lot? Why?

A. The power will be the same regardless of the level of compliance.

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