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. If a hypothesis test were conducted, which of the following statement about the power of the test is true. Check all that apply.

  
I) The power of the test will be greater when the state regulators increase the sample size from 30 to 80 cars in the hypothesis test procedure. WHY? A larger sample size increases the power of the test.

II) The power of the test will be greater when the shop is out of compliance “a lot” than out of compliance "a little". Larger problems are easier to detect.

III) The power of the test will be greater when the state regulators increase the level of significance from 5% to 10%. WHY? There is a greater chance that the null hypothesis will be rejected.

Answer 1

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Answer

:All there are True I, II and III

The power will be greater when when 80 cars are tested. A larger sample size increases the power of the test.

The power will be greater when the shop is out of compliance “a lot”. Larger problems are easier to detect.

The power will be greater when the level of significance is 10%. There is a greater chance that the null
hypothesis will be rejected.