课程名称：统计学 课程性质：必修 课程范围：区间估计与假设检定(单样本与双样本 成对母体 比例) 开课教师：罗光达 开课学院：社科院 开课系级：财政系 考试日期(年月日)：99/4/23 考试时限(Mins)：150Mins 试题本文： Guidance: 1. Do all questions and write legibly. 2. Total point=100; Suggested time=150 minutes. Please keep your original copy of quizzes/midterm/final, in case you need it to correct your scores. 最终答案请务必四舍五入到小数点後第二位。 Question 1 (20%) The real estate assessor for a state government wants to study various characteristics of row houses in the state. A random sample of 75 houses reveals the following: Heated area of the houses (in square feet):X=1801 S=382 40 houses have central air-conditioning. (sample size is small if n<30) (1) Construct a 90% confidence interval estimate of the population mean heated area of the houses. (2) Construct a 95% confidence interval estimate of the population proportion of houses that have central air-conditioning. Question 2 (30%) Let X be N(μ, 500) To test H0: μ = 3000 against H1: μ ≠ 3000. Assume that X = 3050 is the sample mean of a random sample of size 400. (α = 0.05) (1) Use the critical value approach to test this hypothesis. (10%) (2) Use the p-value approach test this hypothesis. (10%) (3) Compute the power of the test at μ = 3010 (10%) Question 3 (30%) 某厂牌行动电话厂商宣称，使用该牌行动电话者，女学生多於男学生至少 10%，今年在200个女学生中有50人使用，另外120个男学生中有19人 使用，(1)请问该厂商之宣称是否有误? (α = 0.05 ) (2)若该厂商宣称男女学生使用行 动电话比例相等，是否有误? (α = 0.05 ) Question 4 (10%) 某人掷一粒骰子48次，出现5点的次数为12次，请问该骰子之5点是否较 其他各点更容易被掷出? (α = 0.05) Question 5 (10%) If you want to be 99% confident of estimating the population mean to within a sampling error of ±5 and the standard deviation is assumed to be 15, what sample size is required? --

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