Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Transcript

應數系高等統計學習題四 1. Let two independent random samples, each of size ten, from two independent normal distributions. N ( 1 , 2 ) and N ( 2 , 2 ) yield x 4.8, s12 8.64, y 5.6, s22 7.88 . (1) Please test the hypothesis H 0 : 1 2 vs. H1:1 2 . (2) Find a 95 percent confidence interval for 1 2 . 2. The following random samples are measurements of the heat-producing capacity （in millions of calories per ton）of specimens of coal from two mines： Mine 1：8,380 8,180 8,500 7,840 7,990 Mine 2：7,660 7,510 7,910 8,070 7,790 (1) Use the 0.05 level of significance to test whether the difference between the means of these two samples is significant. (2) Find a 95 percent confidence interval for the difference of two means. 3. Interval Estimation and Testing Hypothesis Students may choose taking statistics courses from professor A or B. The final written examination is the same for class A and class B. If 13 students in class A and 11 students in class B. Let A and B denote the population mean of class A and class B, respectively, and A2 and B2 denote the variance of class A and class B, respectively. The sample average and standard deviation of each class are Class A： xA 84, s A 4 , Class B： xB 77, sB 6 .（Use 0.1 ） (1) Construct an appropriate statistical hypothesis of testing to judge whether A B . (2) Find a 95 percent confidence interval for the difference of two means. 4. China Airline researcher wants to understand that this company's jade emperor system's result. The researcher extracts n=100 day-long localization record, which is the random sample, and estimates that the mean value which how many people subscribe in advance sit actually but have not ridden by Taipei to Kaohsiung flight every day 4:10PM. Obtains the following data by the record Booking actually but have not ridden ( X ) 0 1 2 3 4 5 6 Number of days 20 37 23 15 4 0 1 Use the Chi-square test to test whether X is Poission distribution. （Use 0.1 ） 5. Some researcher is studying the average life of one kind of the tire. Must first confirm this tire's attrition distance in kilometer in the research first stage whether to become the normal distribution. Its experiment's result is as follows Attrition distance in kilometer(interval) Intermediate points Numbers 23,000 22,500 33 23,000~24,000 23,500 31 24,000~25,000 24,500 66 25,000~26,000 25,500 100 26,000~27,000 26,500 84 27,000~28,000 27,500 57 28,000 28,500 29 Does this one kind of the tire attrition number become the normal distribution? 2 2 (6) 16.81, 0.01 (4) 13.24 ） （Use 0.01 , 0.01