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 type of error would the shop’s owner consider more serious, and why?

A. Type I Error. WHY? They would unjustifiably lose their certification, even though they are meeting the standards.
B. Type II Error: WHY? They would justifiably lose their certification, even though they are meeting the standards.
C. Type I Error: WHY? They would justifiably lose their certification, even though they are meeting the standards.
D. Neither Type I nor Type II error would the repair shop’s owner consider more serious.

Answer 1

according to question, null and alternate hypotheses are :

H0 : vehicles exhaust emissions exceed specified limits for various pollutants.

Ha :   vehicles exhaust emissions not exceed specified limits for various pollutants.

now, type of error the shop’s owner consider more serious would be the TYPE II ERROR , which is the probability of accepting the false null hypothesis and rejecting true alternative hypothesis ,which infact Ha is true .

and conclude that , They would justifiably lose their certification, even though they are meeting the standards.

so, option (B) is correct .

I HOPE I WAS HELPFUL AND HAVE CLEARED YOUR DOUBTS.

THANKYOU .