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 environmentalists consider more serious, and why?

A. Neither Type I error nor Type II error would be of serious concern to environmentalists because the polluting rate is equal to the significance level, α = 0.05.

B. Type I Error: WHY? Shops are allowed to operate even though they are allowing polluting cars to drive the streets.

C. Type II Error. WHY? Shops are allowed to operate even though they are allowing polluting cars to drive the streets.

D. Type I Error. WHY? Shops are not allowed to operate even though they are allowing polluting cars to drive the streets.

Answer 1

according to the problem , the null and alternate hypotheses are :

H0 : vehicles exhaust emissions exceed specified limits for various pollutants, against ,

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

so , in this case , type II error is more serious than type I error ,

because , type II error is probability of accepting the false null hypothesis , and rejecting true alternate hypothesis , which in fact , Ha is true .

so , option (C) is correct , and conclude that , Shops are allowed to operate even though they are allowing polluting cars to drive the streets.

I HOPE I WAS HELPFUL AND HAVE CLEARED YOUR DOUBTS .

THANKYOU