課程名稱︰ 統計學一下 課程性質︰ 必修 課程教師︰ 任立中教授 開課學院： 管理學院 開課系所︰ 國際企業學系 考試日期（年月日）︰ 2010/03/24 考試時限（分鐘）： 約25分鐘 是否需發放獎勵金： 是 （如未明確表示，則不予發放） 試題 : A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each 4 primary specialties - General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) - and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. The president theorizes that foreign graduates will have higher mean charges than USA graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. The result for the ANOVA are summarized in the following table. --- Source df SS MS F PR>F --- Specialty 3 22,855 7,618 60.94 0.0001 Med school 1 105 105 0.84 0.6744 Interaction 3 890 297 2.38 0.1348 Error 152 18,950 --- Total 159 42,800 1. Referring to the Table, what was the total number of doctors included in the study? a) 20 b) 40 c) 159 d) 160 2. Referring to the Table, what degrees of freedom should be used to determine the critical value of the F ratio agianst which to test for interaction between the two factors? a) numerator df=1, denominator df=159 b) numerator df=3, denominator df=159 c) numerator df=1, denominator df=152 d) numerator df=3, denominator df=152 3. Referring to the Table, interpret the test for interaction. a) There is insufficient evidence to say at the 0.10 level of significance that the difference between the mean charges for foreign and USA graduates depends on primary specialty. b) There is sufficient evidence to say at the 0.10 level of significance that the difference between the mean charges for foreign and USA graduates depends on primary specialty. c) There is sufficient evidence at the 0.10 level of significance of a difference between the mean charges for foreign and USA medical graduates. d) There is sufficient evidence to say at the 0.10 level of significance that the mean charges depends on both primary specialty and medical school. 4. Referring to the Table, what degrees of freedom should be used to determine the critical value of the F ratio agianst which to test for difference in the mean charges for doctors among the four primary specialty areas? a) numerator df=1, denominator df=159 b) numerator df=3, denominator df=159 c) numerator df=1, denominator df=152 d) numerator df=3, denominator df=152 5. Referring to the Table, what degrees of freedom should be used to determine the critical value of the F ratio agianst which to test for difference between the mean charges of foreign and USA medical school graduates? a) numerator df=1, denominator df=159 b) numerator df=3, denominator df=159 c) numerator df=1, denominator df=152 d) numerator df=3, denominator df=152 6. Referring to the Table, is there evidence of a difference between the mean charges of foreign and USA medical school graduates? a) Yes, the test for the main effect for primary specialty is significant at α=0.10. b) No, the test for the main effect for primary specialty is not significant at α=0.10. c) No, the test for the interaction is not significant at α=0.10. d) Maybe, but we need information on the β-estimates to fully answer the question. 7. Referring to the Table, what assumption(s) need(s) to be made in order to conduct the test for differences between the mean charges foreign and USA medical school graduates? a) There is no significant interaction effect between the area of primary specialty and the medical school on the doctors' mean charges. b) The charges in each group of doctors sampled are drawn from normally distributed populations. c) The charges in each group of doctors sampled are drawn from populations with equal variances. d) All of the above are neccessary assumptions. --

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