19. What of the following statement is incorrect for a normal random variable X?
(A) The area under a normal curve needs to be less than 1.
(B) The mean and median of X are equal.
(C) The mean and mode of X are equal.
(D) The normal curve is symmetry about mean.
(E) The probability above the mean and below the mean has to be equal.

20. Assume the secondary fee (X) for a case for a real estate agency in a real estate agency follows a normal distribution with mean 66.2 thousand dollars and standard deviation 4.4 thousand dollars. Which of the following statement is incorrect? (A) The probability of this real estate agency will receive at least 70 thousand dollars equals 0.1949. (B) The probability of this real estate agency will receive exactly 74.82 thousand dollars equals 0.025. (C) The probability of this real estate agency will receive less than 62.4 thousand dollars equals 0.1949. (D) The probability of this real estate agency will receive less than 66.2 thousand dollars equals 0.5. (E) The probability of this real estate agency will receive more than 62.4 thousand dollars and less than 70 equals 0.6102.

21. What of the following condition is not necessary for the Central Limit Theorem? (A) Each observation has equal mean. (B) Each observation has equal variance. (C) Each observation has to have a normal distribution. (D) Observations are independent. (E) The sample size has to be large.

22. What of the following condition is not necessary for collecting the random samples? (A) Each observation has equal mean. (B) Each observation has equal variance. (C) Each observation has the same distribution. (D) Observations are independent. (E) The sample size has to be large

23. What of the following properties is not true for the sample mean? (A) It is often used to estimate the population mean. (B) The distribution of the sample mean is approximately normal when the sample size is large. (C) The mean of the sample mean equals the population mean. (D) The variance of the sample mean equals the population variance. (E) The observations used to compute the sample mean are independent.

24. What of the following properties is not true for the sample mean? (A) It is often used to estimate the population mean. (B) The distribution of the sample mean is approximately normal when the sample size is large. (C) The mean of the sample mean equals the population mean. (D) The variance of the sample mean equals the population variance. (E) The observations used to compute the sample mean are independent.

25. The Tourism Bureau of Taiwan, would like to estimate the mean amount of money spent by a tourist to within $1000 with 95% confidence. If the amount of money spent by tourists is considered to be normally distributed with a standard deviation of $2000, what sample size would be necessary for the Chamber of Commerce to meet its objective in estimating this mean amount? (A) 4 (B) 6 (C) 8 (D) 11 (E) 16

26. What of the following properties is not true for the t distribution? (A) As the degrees of freedom increase, the t distribution is nearly identical to the standard normal distribution. (B) The mean of the t distribution equals 0. (C) The t distribution is bell shaped. (D) The t distribution is symmetric about 0. (E) The t distribution has thinner tails than the standard normal distribution.

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.

28. Which is the most appropriate statistical test to evaluate the association between the data for the location (Urban and Rural) and house value (unit: thousand dollars)? (A) Chi-square test (B) F test (C) McNemar test (D) Paired T test (E) Two-independent sample T test

29. What of the following condition is not required to construct a regression model? (A) The mean value of each error term equals to 0. (B) The observations are independent. (C) The observations have the common variance. (D) The response variable has a common normal distribution. (E) The response variable has to be linear associated with the explanatory variable.

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