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. 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? d) Which type of error might environmentalists consider more serious? a) What is a Type I error? A. The regulators decide that the shop is not meeting the standards when the shop is not meeting them. B. The regulators certify that the shop is meeting the standards when the shop is meeting them. C. The regulators certify that the shop is meeting the standards when the shop is actually not meeting them. D. The regulators decide that the shop is not meeting the standards when the shop is actually meeting them. b) What is a Type ll error? A. The regulators certify that the shop is meeting the standards when the shop is not actually meeting them. B. The regulators decide that the shop is not meeting the standards when the shop is actually meeting them. C. The regulators decide that the shop is not meeting the standards when the shop is not meeting them. D. The regulators certify that the shop is meeting the standards when the shop is meeting them. c) Which type of error would the shop's owner consider more serious? Type I error Type II error d) Which type of error might environmentalists consider more serious? Type I error Type II error

Explanation / Answer

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is incorrectly retaining a false null hypothesis (a "false negative").[1] More simply stated, a type I error is detecting an effect that is not present, while a type II error is the failure to detect an effect that is present.

null hypothesis - shop meet the standard

alternate - don't meet the standard

a)   type I error is the incorrect rejection of a true null hypothesis

option D) is correct

b) type II error is incorrectly retaining a false null hypothesis

option A) is correct

c) shop oqwner will consider type 1 error more serious as

as regulator decides that the shop does not meet standards

d) environmentalist will consider type 2 error more serious as

the shop is certified to meet the standard when it is not .

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