Which of the following statements INCORRECT? A. If X_1, X_2, ..., X_n is a rando

Question

Which of the following statements INCORRECT? A. If X_1, X_2, ..., X_n is a random sample of size n taken from a normal population with mean mu and variance sigma^2, then X ~ N(mu, sigma^2/n) where X = x_1 + x_2 + ...+ X_n/n. B. One nice property of Maximum likelihood estimator (MLE) of parameter theta is that MLE is approximately an unbiased estimator for theta when sample size n gets large. C. When solving for MLE, maximizing the likelihood function L(theta) is equivalent to minimizing the logarithm of the likelihood function. D. None of the above. An upper confidence bound on the mean of a normal distribution with known variance sigma^2 is is X - 1.5 sigma/Squareroot n lessthanorequalto mu lessthanorequalto x + 1.5 sigma/Squareroot n. What is the confidence level? A. 93.32% B. 86.64% C. 13.36% D. None of the above. Suppose the lzod impact strength follows a normal distribution with standard deviation of 0.5. An Izod impact test was performed on 25 specimens of PCV pipe and the sample mean is Construct a 99% two-sided CI on the mean Lzod impact strength. A. 1.135 lessthanorequalto mu lessthanorequalto 1.865 B. 1.242 lessthanorequalto mu lessthanorequalto 1.758 C. 1.267 lessthanorequalto mu lessthanorequalto 1.733 D. None of the above. Which of the following situations is a CORRECTLY stated hypothesis testing problem? A. H_0: s^2 = 30 versus H_1: s^2 > 30 B. H_0: mu = 10 versus H_1: mu notequalto 12 C. H_0:p = 0.3 versus H_1:p

Explanation / Answer

By usual definitions we have

Question-9 Part-D

Question-10 Part-B

Question-11 Part-B

One-Sample Z

The assumed standard deviation = 0.5

N   Mean SE Mean      99% CI

25 1.500    0.100 (1.242, 1.758)

Question-12 Part-C

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