109年 - 109東吳大學_碩士班招生考試_國際經營與貿易學系A組(國際貿易與金融)︰統計學#100389

選擇題 (4)

1. 在一可裝 6 發子彈的左輪手槍裡，只放一顆子彈，隨機地一轉後，要求二位
戰俘輪流用手槍向自己的頭部發射，直到一名戰俘中槍，另一名戰俘才逃過一劫。小
明與小華聽完此情境後，各自發表了看法：
小明說：先發射者比較不利（意旨死亡機率較高）。
小華說：若改為放兩顆子彈，我認為先發者比較不利（意旨死亡機率較高）。(A) 小明說對了，而且小華也說對了。(B) 小明說對了，但小華說錯了。(C) 小明說錯了，但小華說對了。(D) 小明與小華都說錯了。

2. 有甲、乙、丙三囚犯，國王宣佈以抽籤決定釋放其中一位，處決另兩位。國王抽籤完後告訴獄卒哪一位將被釋放，但要求獄卒不可先透露。甲請求獄卒透露哪一位會被釋放，可惜遭到拒絕，於是他改問獄卒『乙及丙中，哪一位會被處決？『獄卒經過一番思考，（誠實地）告訴甲，『乙會遭處決』。獄卒認為這樣做並未違反國王的規定。 (A) 甲聽完獄卒的說法後，他會被釋放的機率提高至 1/2。 (B) 甲聽完獄卒的說法後，他會被釋放的機率提高至 2/3。 (C) 甲聽完獄卒的說法後，他會被釋放的機率依舊不變，仍然是 1/3。 (D) 以上皆非。

3. Consider the following statements about a 95% confidence interval (CI) for a parameter ??.
Statement 1: P(??0 iiii iiii ??ℎe CCCC|?? = ??0) ≥ 0.95
Statement 2: P(??0 iiii iiii ??ℎe CCCC) ≥ 0.95
Statement 3: An experiment produced the CCCC[−1, 1.5]: P(?? iiii iiii [−1, 1.5]|?? = 0) ≥ 0.95.(A) Only Statement 1 is correct.(B) Only Statement 2 is correct.(C) Only Statement 3 is correct.(D) Only Statement 1 is incorrect.
(E) Only Statement 2 is incorrect

4. Consider the linear regression model: y = ??0 + ??1x1 + ??2x2+. . . +??mxm + ??. The data set is
{yii, xii1, xii2, … , xiiii}ii=1 n . After fitting these data into this model, you obtained the linear system which is
denoted by ?? = ???? + ??. Which of the followings is NOT TRUE ?(A)(B) , then we cannot find the least square estimator for ??.(C) Follow the least square criterion, we have the residuals. The sum of residuals must be zero.(D) If you add new independent variable xm+1 into the original linear regression model,
i.e. y = β₀ + β₁x₁ + β₂x₂+. . . + + ε, then the coefficient of determination won’t
decrease.

申論題 (14)

1. What is the central limit theorem?

2. What is a consistent estimator?

3. What is a type II error?

4. What is the purpose to calculate the adjusted coefficient of determination?

5. What is the main difference between linear regression and logistic regression?

6. What is the purpose to conduct the Kolmogorov-Smirnov test?

(1) Assume p = 0.5. Use the central limit theorem to estimate the probability that in a poll of 25 people, at least 14 people support the referendum. Your answer to this problem should be a decimal (up to thousandths place).

(2) With p unknown and n the number of random people polled, let be the fraction of the polled people who support the referendum. What is the smallest sample size n in order to have a 90% confidence that is within 0.01 of the true value of p? Your answer to this problem should be an integer

2. Someone claims to have found a long-lost work by Jane Austen. She asks you to decide whether
or not the book was actually written by Austen. You buy a copy of Sense and Sensibility and count the
frequencies of certain common words on some randomly selected pages. You do the same thing for the
‘long-lost work’. You get the following table of counts.

Using this data, set up and evaluate a significance test of the claim that the long-lost book is by Jane Austen. Use a significance level of 0.1.

(1) Find the least square estimator for c and d in the Model 1.

(2) Find the least square estimator for c and d in the Model 2.

(3) Find (sum of squared residuals of the Model1).

(4) Find (sum of squared residuals of the Model 2).

(5) Find (coefficient of determination in Model 1 and in Model 2 respectively). (6) According to the value of R², which Model (Model 1 or Model 2) is better?

109年 - 109東吳大學_碩士班招生考試_國際經營與貿易學系A組(國際貿易與金融)︰統計學#100389

試卷資訊

選擇題 (4)

申論題 (14)