課程名稱︰統計導論 課程性質︰數學系選修 課程教師︰江金倉 開課學院：理學院 開課系所︰數學系 考試日期（年月日）︰2017.1.4 考試時限（分鐘）：50 試題 : Introduction to Staatistics (Test 4) 1.(20%) State or define the following terms: (1a) statistic. (1b) confidence interval. (1c) significance level. (1d) power function. (1e) probability function. 2.(10%) Let X_1, X_2,..., X_n be a random sample from a normal distribution with mean μ and variance σ^2. Let φ=Σ_{i=1}^{n}X_i/n and τ^2=Σ_{i=1}^{n} (X_i-φ)^2/(n-1). What are the distributions of (n-1)(τ/σ)^2 and √n(φ-μ)/τ. 3.(10%) Let X be a random variable from a normal distribution with mean μ and known variance σ^2. Find the sample size required to achieve P(|φ-μ|≦E) =1-α, where φ is the sample mean. 4.(10%) Let W_n be a test statistic such that large values of W_n tend to reject the null hypothesis. Define a reasonable p-value based on W_n. 5. Let x_1,...,x_n be observed sample values from a normal distribution with mean μ and variance σ^2, where μ and σ^2 are unknow constants. (5a)(10%) Construct a (1-α), 0<α<1, confidence interval for μ. (5b)(10%) Construct a (1-α), 0<α<1, confidence interval for σ^2. (5c)(10%) Consider the null hypothesis H_0:μ=μ_0 versus the alternative hypothesis H_A:μ>μ_0. What is the p-value of the corresponding hypothesis? 6. Let (X_11,...,X_1(n_1)) and (X_21,...,X_2(n_2)) be two independent random samples from N(μ_1,σ^2) and N(μ_2,σ^2), respectively. (6a)(10%) Construct a (1-α), 0<α<1, confidence interval for μ_1-μ_2. (6b)(10%) State the testing procedure for the hypothesis H_0:μ_1=μ_2 versus H_A:μ_1≠μ_2 with the significance level α. --

※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 140.112.249.45 ※ 文章網址: https://webptt.com/m.aspx?n=bbs/NTU-Exam/M.1486799349.A.641.html