5.1 PROBLEMS 287 algebra according to a new method. Find a 90% confidence interval for the difference in achievement scores expected from the two methods. Method Students' Achievement Scores d Present 68 72 79 69 60 68 84 80 78 New r, 64 5), 73 72 70 Diet A was given to four overweight girls and diet B was given to five other overweight girls, with the following observed weight losses. Find a 90% confidence interval for mean ), ). difference in effectiveness of the two diets. ARVE $2 MD Diet Weight Losses (pounds) A s 7, 2, -1, 4 6, 5, 2, 8, 3 В r 5. Eight volunteers for an experiment are divided randomly into two groups, to see if a telescopic sight improves the ability to hit a target under twilight conditiorns. Group A is given rifles with telescopic sights, while group B has the same kind of rifle but with open sights. After a learning period they are given a shooting test at twilight. These are their scores (100 is perfect). Group A Group B: 96 93 89 83 77 conclude? (R you What do 6Ten tents using plain camouflage and 10 tents using patterned camouflage are set up in a wooded area, and a team of observers is sent out to find them. The team reports the distance at which they first sight each tent (true sightings only) until all 20 tents are found. The purpose of the study is to determine whether the patterned camouflage is more difficult to detect than the plain camouflage. The distances at which each tent is detected are reported as follows. Distance (meters) Type of camouflage 25, 28, 16, 34, 38, 21, 29, 43, 32, 36 26, 12, 16, 21, 20, 14, 10, 18, 22, 20 Plain Patterned (a) Perform a hypothesis test. (b) Find a nonparametric 95% confidence interval for the difference in mean detection distances. anoil PROBLEMS 1. Let S equal the number of pairs (Xy Y) in which X exceeds Y, (counting ties as one-half). S =T-n(n+ 1) 2 Note that there are mn pairs in all. Show that S and T satisfy the relationship What statistic seems reasonable to use as an estimate of P(X> Y)? 8 80