区间估计与本数(二).doc

區間估計與樣本數(二) In statistical estimation, the ratio of two unknown variances can be estimated through (A) at distribution (B) a chi-square distribution (C) an F distribution (D) the standard normal distribution (E) not necessary any of (A) to (D) A survey was taken of U.S. companies that do business with firms in India. One of the questions on the survey was： Approximately how many years has your company been trading with firms in India？ A random sample of 44 response to this question yielded a mean of 10.455 years. Suppose the population standard deviation for this question is 7.7 years. Using this information, construct a 90% confidence interval for the mean number of years that a has been trading in India for the population of U.S. companies trading in India. The amounts (in ounces) of juice in eight randomly selected juice bottles are： 15.7, 15.3, 15.6, 15.3, 15.4, 15.0, 15.6, 15.4 Find a 95% confidence interval for the standard deviation, σ, of the amounts of juice in all such bottles. (A) 0.13 to 0.46 (B) 0.22 to 0.46 (C) 0.15 to 0.45 (D) 0.18 to 0.69 (E) 0.02 to 0.21 某公司由一批重量是服從常態分配的產品中隨機取10件，測量各件產品的重量(公斤)，以瞭解產品重量的變異。此10件產品重量分別是6.1, 5.7, 6.0, 5.9, 5.8, 6.3, 5.8, 6.1, 5.9, 6.2。試求： (1) 此公司產品重量的變異數之點估計？ (2) 此公司產品重量的變異數之90%信賴區間？ (3) 此公司產品重量的標準差之95%信賴區間？ Let be a random sample from with known mean μ. Describe how you would construct a confidence interval for the unknown variance . 自母體為Bernoulli(P)分配中抽取隨機樣本。已知，請估計母體P之95%的信賴區間為__________。若要求上題之區間長不超過10%，則在相同的信賴度下，應再加抽多少個樣本__________。 某調查機構正規劃一項「總統候選人支持度」調查，委託單位要求在95%信心水準下，推論的誤差範圍必須控制在之內，請問該調查機構至少須完成多少有效樣本才能符合規定？若委託單位要求在99%信心水準下，推論的誤差範圍必須控制在之內，則該調查機構至少須完成多少有效樣本才能符合規定？ A research paper reports the percentage of people 18 years of age and older who smoke. Assume that a study is being designed to collect new data on smokers and nonsmokers. The best preliminary estimate of the population proportion that smoke is 30%. (1) Using 95% confidence, the sample size that should be taken to estimate the proportion of smokers