27. What of the following properties is true for the confidence interval? (A) As the confidence level gets larger, the length of confidence interval tends to be shorter. (B) As the mean gets larger, the length of confidence interval tends to be shorter. (C) As the sample size increases, the length of confidence interval tends to be shorter. (D) As the variance gets larger, the length of confidence interval tends to be shorter. (E) The confidence interval has the same length regardless of the random samples.

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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