5. (5%)在簡單線性迴歸分析中’若X與Y變數之相關係數爲0_9，則表示可解釋變 異有
(A) 90%
(B) 81%
(C) 10%
(D) 19%

1. (5%)投擲二個相同公正骰子’出現的點數和爲6的機率爲

2. (5%)設X1 ~N(0,l) , X2 ~N(0,1)，P(X1 +X2 ＞2) = (A)0.025(B)0.0933 (C) 0.1587 (D)無法決定

3. (5%)欲估計台北市市民對奢侈稅政策的支持度，抽訪1068位市民中有534位支 持奢侈稅政策，貝！J信賴度95%的估計誤差界限爲 (A) 5% (B)3% (C) 2.5% (D) 95%

4. (5%)某飲料製造商宣稱其產品DEHP塑化劑之溶出量低於l.f ppm，欲檢定其宣 稱，則下列何者正確？ (A)H0 : ju ≥ 1.5 (B) H0 : ju ≤ 1.5 (C) H0 : ju ＜1.5 (D) H0 : // ＞ 1.5

25.The distribution for X is uniform. What can we say for certain about the distribution for ΣX when sample size n=50? (A)distribution for ΣX is still uniform with the same mean and standard deviation as the distribution for X. (B)distribution for ΣX is still uniform with the larger mean but a smaller standard deviation as the distribution for X. (C)The distribution for ΣX is normal with the same mean but a larger standard deviation as the distribution for X. (D)The distribution for ΣX is normal with a larger mean and a larger standard deviation than the distribution for X. (E)The distribution for ΣX is normal with the same mean but a smaller standard deviation than the distribution for X.

24.Part of an ANOVA table is shown below. The sample size is (A)4 (B)5 (C)18 (D)22 (E)None of the above.

23.Let (Yᵢ, xᵢ), i=1,2,...,n, be a random sample. (A)Since the sample correlation coefficient is found to be r=0.9, simple linear regression model would be suitable for modelling the relationship for Y and x. (B)It is further known that both the sample standard deviations of Y and x are 1's, then the estimated regression coefficient would be 0.9. (C)Normal distribution assumption is a must for the error term if we want to find the least squares estimate. (D)A significant result can be obtained if r=0.9, because the value is large enough. (E)None of the above.

22.The following sum of squares are produced.  Σ(yᵢ-ȳ)²=200, Σ(yᵢ-ŷᵢ)²=80, and Σ(ŷᵢ-ȳ)²=120. The percentage of the variation in y that is explained by the variation in x is (A)25% (B)80% (C)33% (D)60% (E)66%

21.Suppose that X is a discrete random variable taking on the values of 0, 1 and 2, and the corresponding probability function f(·) is such that 2f(0)=f(1)=f(2). Then, the expected value of X is (A)1/5 (B)2/5 (C)4/5 (D)1 (E)6/5

20.An insurance company sets up a statistical test with a null hypothesis that the average time for processing a claim is 7 days, and an alternative hypothesis that the average time for processing a claim is greater than 7 days. After completing the statistical test, it is concluded that the average time exceeds 7 days. However, it is eventually learned that the mean process time is really 7 days. What type of error occurred in the statistical test? (A)random error (B)margin of error (C)Type II error (D)Type I error (E)No error occurred in the statistical sense.

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