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.

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.

38. Suppose that a 99% confidence interval for the difference $p_1 - p_2$ between the proportions of men and women in Taiwan who are alcoholics equals (0.02, 0.09). (A) We are \( 99\% \) confident that the proportion of alcoholics is between 0.02 and 0.09. (B) We are \( 99\% \) confident that the proportion of men in Taiwan who are alcoholics is between 0.02 and 0.09 larger than the proportion of women in Taiwan who are. (C) We can conclude that the population proportions may be equal. (D) We are \( 99\% \) confident that a minority of Taiwan residents are alcoholics. (E) Since the confidence interval does not contain 0, it is impossible that \( p_1 = p_2 \)

39. Which of the following statement is when the one-way ANOVA provides relatively more evidence that $H_0: \mu_1 = \mu_2 = \cdots = \mu_g$ is rejected? (A) The smaller the between-groups variation. (B) The smaller the within-groups variation. (C) The larger the between-groups variation. (D) The larger the within-group variation. (E) None of the above.

40. Which of the following statement about coefficient of determination $R^2$ is incorrect? (A) As the number of explanatory variables increases, \( R^2 \) may increase. (B) It provides the percentage of explained variance in the response variable using the regression model. (C) Its value must fall in 0 and 1. (D) The correlation of coefficient must equal to \( R^2 \). (E) When \( R^2 = 1 \), the response variable has an exact linear relationship with the explanatory variable in the simple regression model.

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