12. Incorrect. The answer is false, not true

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

H₀: β₀ = 40

H₁ β₁ ≠ 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 - b₀) / (s_b/ √T) < t_{a/2, n-1}] = 99 %

P [ -t_{0.005, 17} < (45 - 40) / (8/ √18) < t_{0.05, 17}] = 99 %

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 b₀ = 40 mg/m³

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