課程名稱：統計學 課程性質：必修 課程範圍：區間估計與假設檢定(單樣本與雙樣本 成對母體 比例) 開課教師：羅光達 開課學院：社科院 開課系級：財政系 考試日期(年月日)：99/4/23 考試時限(Mins)：150Mins 試題本文： 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. 最終答案請務必四捨五入到小數點後第二位。 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%) 某廠牌行動電話廠商宣稱，使用該牌行動電話者，女學生多於男學生至少 10%，今年在200個女學生中有50人使用，另外120個男學生中有19人 使用，(1)請問該廠商之宣稱是否有誤? (α = 0.05 ) (2)若該廠商宣稱男女學生使用行 動電話比例相等，是否有誤? (α = 0.05 ) Question 4 (10%) 某人擲一粒骰子48次，出現5點的次數為12次，請問該骰子之5點是否較 其他各點更容易被擲出? (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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