Tutorial6ConfidenceIntervalEstimation统计学作业六.docxVIP

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Tutorial6ConfidenceIntervalEstimation统计学作业六.docx

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Tutorial 6_Confidence Interval EstimationQuestion 1:The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. It is known from the manufacturer’s specifications that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.995 gallon.a)Construct a 99% confidence interval estimate of the population mean amount of paint included in a 1-gallon can.b)On the basis of your results, do you think the manager has a right to complain to the manufacturer? Why? c)Must you assume that the population amount of paint per can is normally distributed here? Explain.d)Construct a 95% confidence interval estimate. How does this change your answer to (b)?Answer:a)设置信区间为- + ，由题可知，置信水平1-a=99%，所以 a=0.01，= -2.58，± =0.995±（-2.58）= 0.995±0.007所以置信区间为{0.988 ， 1.002}b)没有权利，因为从抽查的结果可以看出，制造商保证了99％的商品含量在1加仑左右，所以经理没有权利控诉。c)不用假设，因为采取的抽取样本数量为大样本，样本均值的抽样分布是正态分布的，所以不需要假设它一定是均匀分布。d)设置信区间为 - + ，由题可知，置信水平1-a=95%，所以a=0.05，= -1.96，± =0.995±（-1.96） = 0.995±0.006所以置信区间为{0.989 ，1.001}。随着置信区间的改变，产品的置信度达到95％时，产品的置信区间仍然在经理允许的0.02的范围内，所以经理没有权控诉。Question 2:In New York State, saving bank are permitted to sell a form of insurance called Saving Bank Life Insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible request for additional medical information and medical exams, and a policy compilation stage where the policy pages generated and send to the bank for delivery. The ability to deliver the approved policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of 1 month, a random sample of 27 approved policies was selected INSURANCE and the total processing time in days recorded:73 19 16 64 28 28 31 90 60 56 31 56 22 18 45 48 17 17 17 91 92 63 50 51 69 16