区间估计与样本数(二).doc

區間估計與樣本數(二)1. 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)2. 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.3. 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, 15.4Find a 95% confidence interval for the standard deviation, , 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 0.214. 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？5. Let be a random sample from with known mean . Describe how you would construct a confidence interval for the unknown variance .6. 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_。7. 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？8. 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 in the population with a margin of error 0.02 is _. (rounding to an integer)(2) Assume that the study uses your sample size recommendation given above and finds 520 smokers. Then the 95% confidence interval for the proportion of smokers in the population is _.9. While conducting a survey on a trial of a new cosmetic product for a company, you choose a confidence coefficient of 0.9 and allowable error of 10%. On the conservative side, what sample size is needed？10. The proportion of junior executives leaving large manufacturing companies within three years is to be estimated within 3 percent. The 0.95 degree of confidence is to be used. A study conducted several years ago revealed that the percent of junior executives leaving within three years was 21. To update this study, the files of how many junior executives should be studied？(A) 594(B) 612(C) 709(D) 897(E) None of the above11. A bank wishes to estimate the mean balances owed by customers holding MasterCard.The population standard deviation is estimate to be $300. If a 98 percent confidence interval is used and an interval of $75 is desired, how many cardholders should be sampled？(A) 44(B) 212(C) 629(D) 87(E) None of the above12. Use the following to answer questions (1)-(2)：A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week.(1) Assuming a standard deviation of 6 hours, what is the required sample size if the error is to be less than 1/2 hour with a 95% level of confidence？(A) 554(B) 130(C) 35(D) 393(E) None of the above(2) Assuming a standard deviation of 3 hours, what is the required sample size if the error is to be less than 1/2 hour with a 99% level of confidence？(A) 196(B) 240(C) 15(D) 16(E) None of the above13. Suppose you wanted to estimate a binomial proportion, p, correct to within .01 with probability 0.95. What size sample would need to be selected？14. 某有線電視想暸其6PM至7PM新聞節目之收視率，乃在市場上進行抽樣調查。假設該公司要求樣本比例與母體比例之誤差不能超過0.01，且有95%之信賴水準，試問樣本數最少應為多少。15. A student in public administration wants to determine the mean amount members of city councils in large cities earn per month as remuneration for being a council member. The error in estimating the mean is to be less than $100 with a 99 percent level of confidence. The student found a report by the Department of Labor that estimated the standard deviation to be $1,000. What is the required sample size？16. A random sample of 16 statistics examinations was taken. The average score, in the sample, was 76.2 with a variance of 144.(1) The 99% confidence interval for the true average examination score is：_.(2) The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is：_.17. We wish to estimate the population proportion. We want to be 95 percent confident of our results and we want the estimate to be with .01 of the population parameter. No estimate of the population proportion is available. What values should we use for p？(A) 1.96(B) 0.01 (C) 0.5(D) We cannot complete the problem, we need more information.18. A bottling machine can be regulated so that it discharges a