(a) (10 分) State the null and alternative hypotheses for a one-sample t-test.

(b) (10 分) Conduct the t-test at a significance level of α=0.05. Include the calculation of the test statistic and the decision rule.

ii. (2 分) 試求條件期望值 E[X|X > 2]。

一、 Critical Thinking and Writing (50%) In recent years, Taiwanese government has launched the Bilingual 2030 policy to boost the competiveness of the next generation in the hope of assisting young people in getting greater employment opportunities both locally and internationally. The use of EMI (English as a medium of instruction) is often thought as a solution to enhancing students' English proficiency and is associated with discourses on internationalization in higher education reform. With more universities regarding EMI as indispensable, the swift expansion of EMI in Taiwan poses many challenges to the implementation of classroom teaching and leads to heated debates and much controversy.  Please write an essay to illustrate your own experience, observation, or argument regarding the advantages or disadvantages of an EMI classroom. You are expected to write at least two paragraphs.

二、 Essay Writing (50%) ChatGPT has been regarded as a landmark progress for artificial intelligence (AI). Based on the following descriptions about ChatGPT, how would you apply it in your English class to facilitate students' learning?

二、假設某個股報酬率服從常態分配，已知其平均報酬率為 10%，標準差 0.15，則其未來一年報酬 率大於 40%的機率為何？(P(Z ≤ 2) = 0.9772)(8 分)

(a) x之機率質量函數(probability mass function)？ (6 分)

(b)期望值與變異數？(6 分)

四、某燈泡廠商宣稱其製造之燈泡不良率小於 8%，某位買主想要檢定一批燈泡不良率是否符合廠商之宣稱，買主從該批產品隨機抽出 100 件檢查，發現有 6 件瑕疵品，試檢定在 95%信賴水準 下，該燈泡廠商製造之燈泡不良率是否小於 8%？(Z0.05 = 1.645，Z0.025 = 1.96) (8 分)

(a)試檢定H0： =0.68)(5 分)

(a)試求 A=？ (6 分)

114年 - 114 國立嘉義大學_碩士班(乙組)招生考試試題_應用數學系：機率統計#144147

110年 - 110 國立臺灣大學_碩士班招生考試_應用數學科學研究所數理統計組:機率統計#102196