## Question

###### (a) [15pts] An experiment was done to test method for reducing faults on telephone lines (Welch 1987). Ten matched pairs of areas were used: The following table shows the fault rates for the test areas (X) and for the control areas (Y):Test (X) 676 206 230 256 280433 337 466 497 512 Control (Y): 88 570 605 617 653 2913 924 286 1098 982(i) Compute the mean difference construct 98 % confidence interval for the true mean difference of fault rates in the test; and control areas_(ii) Using (i) to co

(a) [15pts] An experiment was done to test method for reducing faults on telephone lines (Welch 1987). Ten matched pairs of areas were used: The following table shows the fault rates for the test areas (X) and for the control areas (Y): Test (X) 676 206 230 256 280433 337 466 497 512 Control (Y): 88 570 605 617 653 2913 924 286 1098 982 (i) Compute the mean difference construct 98 % confidence interval for the true mean difference of fault rates in the test; and control areas_ (ii) Using (i) to conclude at a = 0.02 whether the mean differences are different from zero (b) [10 pts] Biological effects of magnetic fields are matter of current concern and research: Inan early study of the effects of strong magnetic field on the development of mice in 5 cages, each containing three 30-day-old albino female mice were subjected for period of 12 days to field with an average strength of 80 Oe/cm. Thirty other mice in similar cages were NOT placed in a magnetic field and served as controls The following table shows the weight gains in grams, for each cage Magnetic Field present (X): 22.8 10.2 20.8 21.3 12.1 Magnetic Field Not present (Y): 23.5 19.5 21.0 18.5 Use the Mann-Whitney test to compare the two weight gains testing the following hypothesis: Ho: X and Y have identical distributions H;:There distributions are dif ferent Conclude at ( 0.10