109年 - 109 國立高雄大學_碩士班招生考試_金融管理學系：統計學#103277

(1) What is the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence?

(2) What is the probability a person admitted to the hospital will die from a treatment-caused injury?

(3) In the case of a negligent treatment-caused injury, what is the probability a malpractice claim will be paid?

(1) Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default.

(2) The bank would like to recall its card if the probability that a customer will default is greater than 0.20. Should the bank recall its card if the customer misses a monthly payment? Why or why not?

(1) The desired margin of error is $0.10.

(2) The desired margin of error is $0.07.

(1) With a 0.02 level of significance and a sample of 30 cars, what is the rejection rule based on the value of x for the test to determine whether the manufacturer’s claim should be rejected?

(2) What is the probability of committing a Type II error if the actual mileage is 23 miles per gallon?

(3) What is the probability of committing a Type II error if the actual mileage is 25.5 miles per gallon?

(1) Use a 0.05 level of significance. Can you conclude that the population means differ?

(2) What is the 95% confidence interval estimate of the difference between the population means?

6. (8%) A survey asked the following question: do you favor or oppose providing tax-funded vouchers or tax deductions to parents who send their children to private schools? Of the 2010 individuals surveyed, 905 favored the proposal, 1045 opposed the proposal, and 60 offered no opinion. Do the data indicate a significant difference in the preferences for the financial support of parents who send their children to private schools? Use a nonparametric method and a 0.05 level of significance.

(1) What is horizon Technology’s market beta?

(2) Test for a significant relationship at the 0.05 level of significance.

(1) Is b an unbiased estimator ofβ?

(2) According to Gauss-Markov Theorem, is b a BLUE (Best Linear Unbiased Estimator) of β?
Please explain.

(1) If one omits the variable ??2 in the regression model, what will the estimated coefficient and be affected?

(2) If one includes one more unnecessary variable X₃ into the true model, what will the estimated coefficient be affected?

10. (10%) There are some red and white balls in a basket. Now we randomly select one ball from the basket with replacement until we obtain a red ball. Let Xi be the number of balls we select from the basket before we get the red ball. The whole process is repeated for n times, which means that we can have ( X₁, X₂, X_3......., Xn) as a sample. Please use MLE to find out the estimator of the ratio R, where

109年 - 109 國立高雄大學_碩士班招生考試_金融管理學系：統計學#103277

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