区间估计与样本数(一).doc

區間估計與樣本數(一)1. 欲比較某一多事故路段加強執法前後違規超速車輛佔通過車輛數之比率，經抽樣調查發現，加強執法前違規之比率16%，加強執法後則降至7%，若兩次抽樣調查之樣本數皆為400，試求：(1) 加強執法前違規超速之比率的99%信賴區間。(2) 加強執法後違規超速之比率的99%信賴區間。(3) 加強執法後下降比率之99%信賴區間。2. The 95% confidence interval estimate of the mean time taken to process a new insurance policy is days. Which one of the following statement is true?(A) Only 5% of all policies take less than 11 days or more than 12 days to process.(B) Only 5% of all policies take between 11 and 12 days to process.(C) About 95 out of every 100 intervals similarly constructed from samples of same size will contain the true mean value.(D) The probability is 0.95 that lies between 11 and 12 days.(E) All of the above.3. Suppose 95% confidence interval for turns out to be (1000, 2100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in reduced interval width?(A) Increase the sample size.(B) Decreases the confidence level.(C) Increase the sample size and decrease the confidence level.(D) Increase the confidence level and decrease the sample size.4. A market survey was conducted to estimate the proportion of home-makers who could recognize the brand name of a cleanser based on the shape and color of the container. Of the 1,400 home-makers, 420 were able to identify the brand name.(1) Using the 0.99 degree of confidence, the population proportion lies within what interval?(2) What are the confidence limits?(3) Interpret your findings.5. A survey of 1,000 randomly sampled citizens found that 650 of these citizens would support a traffic policy. Assuming that the population is infinite, what is the 95% confidence interval for the percentage of support for the policy? (以數字寫出計算公式即可，不必算到最後的答案)6. NSYSU Bookstore decided to sample the dollar amount of individual morning and evening purchases. The manager believes that this information would help her or him develop a new marketing strategy. The data is given in the table below:MorningEvening Find a 95% confidence interval estimate for the difference between the average purchase amounts for the two times of day.7. In a random sample of 100 observations, . The 95.44% confidence interval foris(A) 0.122 to 0.278(B) 0.164 to 0.236(C) 0.134 to 0.266(D) 0.120 to 0.2808. A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. the 95% confidence interval for the true proportion of people who favors Candidate A is(A) 0.722 to 0.878(B) 0.762 to 0.838(C) 78.04 to 81.96(D) 62.469 to 97.5319. The mean weight of trucks traveling on a particular section of 1-475 is not known. A state highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 3.8 tons. What is the 95 percent interval for the population mean?(A) 14.7 and 16.9(B) 13.2 and 17.6(C) 10.0 and 20.0(D) 16.1 and 18.1(E) None of the above10. A market survey was conducted to estimate the proportion of home-makers who could recognize the brand name of a cleanser based on the shape and color of the container. Of the 1,400 home-makers, 420 were able to identify the brand name. Using the 0.99 degree of confidence, the population proportion lies within what interval?11. Given sample statistics of , s = 12 , n = 64 , the point estimate of the population mean and the 95 percent confidence interval are(A) Point estimate = 72 and 95 percent confidence interval equal to (B) Point estimate = 72 and 95 percent confidence interval equal to (C) Point estimate = 70 and 95 percent confidence interval equal to (D) Point estimate = 70 and 95 percent confidence interval equal to (E) None of the above answer is correct.12. A call center manager measures the standard deviation in waiting time for a random sample of 16 customers to be 80 (seconds). Assuming that the waiting times are no