# 287 5.1 PROBLEMS 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 and Present 68 78 72 79 80 69 84 New 64 70 60 72 68 73 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. a), 4. 3). a \$.2 37 an Diet Weight Losses (pounds) 7, 2, -1, 4 6, 5, 2, 8, 3 A er В 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 conditions. Group A is given rifles with telescopic sights, while sights. After a learning period they are given a shooting test at twilight. These are their scores (100 is perfect). open B has the same kind of rifle but with group Group A: Group B: 85 93 88 77 83 80 What do you conclude? up in Ten tents using plain camouflage and 10 tents using patterned camouflage are set 6. 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 ternt is detected are reported as follows. MNH 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. enoi OBLEMS 1. Let S equal the number of pairs (X, Y) in which Xi exceeds Y, (counting ties as one-half). Note that there are mn pairs in all. Show that S and T satisfy the relationship S =T_n(n + 1) 2 What statistic seems reasonable to use as an estimate of P(X> Y)? 96 89 ger, 75)

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