数系高等统计学习题四.doc

應數系高等統計學習題四之詳解 Let two independent random samples, each of size ten, from two independent normal distributions. and yield . Please test the hypothesis . Find a 95 percent confidence interval for . sol： (1) test statistic： test rule：reject if Reject at level. There is sufficient evidence to show that. (2) 95％ C.I. for is 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 Use the 0.05 level of significance to test whether the difference between the means of these two samples is significant. Find a 95 percent confidence interval for the difference of two means. sol： (1) first test test statistic： test rule：reject if or Do not reject at level. There is not sufficient evidence to show that . second test test statistic： test rule：reject if Reject at level. There is sufficient evidence to show that. (2) 95％ C.I. for is 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 and denote the population mean of class A and class B, respectively, and and denote the variance of class A and class B, respectively. The sample average and standard deviation of each class are Class A：, Class B：.（Use ） Construct an appropriate statistical hypothesis of testing to judge wheth