SUBJECTS: Advanced Statistics DIRECTION: Answer the following questions. Show your step by step solution and put some explanation on how you solve it. A. Test for the difference of means from independent sample when the population variance are unknown Z = (x- y)- do σε στ n m Where: z = z statistics d= difference between the two paired of observations σ=population standard deviation n-sample size 1. Two methods of teaching statistics are being tried by a professor. A class of 40 students is taught by method A and a class of 36 is taught by method B. The two classes are given the same final examination. The mean scores are 78 and 74, respectively. Using a 0.05 significance level, can we conclude that the average final examination scores produced by the two methods are different if the population standard deviation is 5? 2. All freshmen in a particular school were found 0 have variation in grades expressed as a standard deviation of 3, two samples among these freshmen, made up to 20 and 50 students each, were found to have means of 88 and 85, respectively. Based on their grades, is the first group really brighter than the second group at 0.01 level of significance? B. Test for the difference of means from independent samples when the population variance is unknown and the sample are more than 30. Z. (x-y)- d V n S + m Where: z = z statistics d= difference between the two paired of observations s-sample standard deviation n & m -sample size 1. The average grade of 50 senior students in statistics is 85 with a standard deviation of 10.2, while a group of 60 senior students got an average of 80 with standard deviation of 8.9. Can the difference in the mean grade be attributed to chance, using 0.05 level of significance? 2. A women's group claims that female college graduates who go to work were paid less than their male counterparts. They cite the results of a study of 1995 college graduates who went to work immediately upon graduation. A total of 32 women are currently making a mean salary of 85,952 with a standard deviation of 1,328, while 40 male graduates are currently making an average of 92,328 with a standard deviation of 809, obtain a 99% confidence interval of the true difference in mean salary for men and women. Does the result substantiate the women's group's claim?