An environmental protection agency conducts a hypothesis test to determine if the mean level of a harmful chemical, μ\muμ, in a local lake exceeds the safe limit of 12 mg/L.
The hypotheses are:
H0:μ≤12 H_0: \mu \le 12 H0:μ≤12 H1:μ>12 H_1: \mu > 12 H1:μ>12Based on a sample, the agency does not find sufficient evidence to reject H0 H_0\,H0 and declares the lake safe. However, the true mean concentration of the chemical is actually 14.5 mg/L. Which of the following correctly describes the error made by the agency?
A Type I error, because they rejected H0H_0H0 when it was actually true.
A Type I error, because they failed to reject H0H_0H0 when it was actually false.
A Type II error, because they rejected H0H_0H0 when it was actually true.
A Type II error, because they failed to reject H0H_0H0 when it was actually false.
