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.

30. A real-estate agent would like to know whether renovation in an area would increase the house value. He randomly selects a sample of houses before renovation. He evaluates the house value before and after renovation. Which is the most appropriate statistical test to answer this question? (A) Chi-square test (B) F test (C) McNemar test (D) Paired T test (E) Two-independent sample T test

31. Consider the problem of time use for housework for female and male. The time is reported by the average number of minutes per day spent on cooking and washing up. The following provides some summary statistics: Which of the following statement is the most appropriate statement? (A) The average time use for women is significantly different than that for men. (B) The average time use for women is significantly higher than that for men. (C) The average time use for women is significantly lower than that for men. (D) The average time use for women is similar to that for men. (E) The information is not sufficient to make any inference.

32. Suppose a potential customer would like to evaluate where there exist difference in house value (unit: thousand dollars) between urban and Rural areas. Let $\mu_1$ and $\mu_2$ denote the average house value for urban and Rural areas. Also, let $\bar{x}_1$ and $\bar{x}_2$ denote the sample mean of house value for urban and Rural areas. Which of the following statement is correct? (A) $H_0: \mu_1 \ge \mu_2$ versus $H_a: \mu_1 < \mu_2$. (B) $H_0: \mu_1 = \mu_2$ versus $H_a: \mu_1 \neq \mu_2$. (C) $H_0: \bar{x}_1 \ge \bar{x}_2$ versus $H_a: \bar{x}_1 < \bar{x}_2$. (D) $H_0: \bar{x}_1 = \bar{x}_2$ versus $H_a: \bar{x}_1 \neq \bar{x}_2$. (E) $H_0: \bar{x}_1 = \bar{x}_2$ versus $H_a: \bar{x}_1 < \bar{x}_2$.

33. Which is the most appropriate test to evaluate the association for the data of the location (Urban and Rural) and the type of housing (Apartment, Single house, Townhouse and Condo)? (A) Chi-square test (B) F test (C) McNemar test (D) Paired T test (E) Two-independent sample T test

34. Which is the correct statement of the null hypothesis to evaluate the association for the data of the location (Urban and Rural) and the type of housing (Apartment, Single house, Townhouse and Condo)? (A) \( H_0 \): Location and type of housing are associated. (B) \( H_0 \): Location and type of housing are dependent. (C) \( H_0 \): Location and type of housing are independent. (D) \( H_0 \): Location and type of housing are uncorrelated. (E) None of the above.

35. When $H_0$ is true in a given test with significance level 0.05, what is the most range for the p-value? (A) Equals to 0.05. (B) Greater than or equal to 0.95. (C) Greater than or equal to 0.05. (D) Less than 0.05. (E) Less than 0.95.

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

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