36. Which of the following statement is correct? (A) A 95% confidence interval for μ = population mean IQ is (96, 110). So, in the test of H_0: μ = 100 versus H_a: μ ≠ 100, the p-value is greater than 0.05. (B) For a fixed significance level α, the probability of a Type II error increases when the same size increases. (C) If we reject H_0: μ = 0 in a study about change in weight on a new diet using a significance level of α = 0.05, then we also reject it using α = 0.01. (D) P[Type II error]=1-P[Type I error] (E) The p value is the probability that H_0 is true.

37. An industrial plant claims to discharge no more than 1000 gallons of wastewater per hour, on the average, into a neighboring lake. An environmental action group took some random samples from the lake over a period of time to analyze the true mean discharge of wastewater per hour exceeded the company claim of 1000 gallons. Consider a one-sided hypotheses and use a significance level of $\alpha = 0.05$. What of the following statement is correct? (A) If the plant is not exceeding the limit, but actually $ \mu = 1000 $, there is only $ 5\% $ chance that we will conclude they are exceeding the limit. (B) If the plant is exceeding the limit, there is only a $ 5\% $ chance that we will conclude that they are not exceeding the limit. (C) If we reject $ H_0 $, the probability that it is actually true is 0.05. (D) The probability that the sample mean equals exactly the observed value would equal 0.05 if $ H_0 $ were true. (E) All of the above.

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