5. A random draw (with replacement) of 1000 balls from a pool of several million balls is conducted. Each ball is cither blue or red. Let p denote the fraction of blue balls in the population. Let denote the fraction of blue balls in the sample. You want to test the competing hypotheses H0: P = 0.4 vs. H1: P ≠0.4. Suppose that you decide to reject Note that the sample of l 000 balls is considered as a large sample. What is the type I error of this test? (A)0.178 (B)0.256(C)0.367 (D) 0.488 (E) 0.519

複選題18. A survey with size of 150 was conducted to investigate whether gender (male versus female) is associated with annual salary (the dependent variable), after controlling for years of experience, years of education, and the position level categorized as "top or middle level manager', "first-line manager", and "non-manager". You want to conduct a multiple linear regression model. Which of the following is/are correct? (A) When testing for the overall significance of the model, the degree of freedom for the critical value of F is (6, 143)； (B) Assuming that we treat "male" as a reference group for the gender variable, the estimated coefficient is interpreted as the additional amount of women's annual salary compared with male's, after years of experiences, years of education, and the position level are held constant； (C) To test whether years of education is significant factor on annual salary after adjusting other variables, we can use t-test with a degree of freedom of 144 to detect whether its estimated coefficient is different from 0； (D) Given that the 95% confidence interval of the coefficient for years of experience is (500, 1000), its estimated coefficient is definitely a positive value； (E) The variable of "position level" has to be converted to a numerical variable by assigning "non-manager" as O, "first-line manager" as 1, and "top or middle level manager" as 2 in order to be included in the regression model.

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