**12. Correct. The answer is
false**

Assuming that the emissions of PM-2.5 follow a normal distribution, the
inspectors only need to test the following hypothesis:

H_{0 }: β_{0 }= 40

H_{1 }: b_{1
}≠
40

since they do not know the
true variance of concentrations they approximate it using the observed sample
variance = 2, consequently they use a *t *statistics:

one tail test

90% confidence interval => 0.99 = 1- a => a = 0.01

T = 18 => d.f. = T-1 =
17

b = sample
mean = 45

s_{b} =
sample standard deviation =
8

P [ -*t _{a/2, n-1} < *(b - b

P [ -*t _{0.005, 17} < *(45 - 40) /
(8/ √18) <

P [ - 2.898*
< *(45 - 40) / (8/ √18) < 2.898] = 99 %

P [ - 2.898* < *2.6516 < 2.898] = 99 %

=> do not reject the null hyphothesis that the true average concentrations of PM-1.5
is b_{0 }= 40 mg/m^{3}

=> Inspectors cannot conclude that you are in violation of environmental regulation.