1. Calculate the standard error of the difference for each of the following sets of independent data. x, x. N, N2 50, so A. 172 175 so 50 20 18 B. 9.7 7.0 10 15 2.5 3.1 2. What are the tvalues for problems 1A and 13? Is either significant? At what level of condence? 3. Define the standard error of the difference. 4. In a study of absolute errors in active versus passive arm positioning, an investigator collected data (in centimeters) on 20 college-age subjects (from the motor learning laboratory, California State University Northridge, courtesy of Tami Abourezk). Does a signicant difference exist in the errors in arm positioning made by the active group (N 1 = 10) compared with those made by the passive group (N2 = 10)? Subject Active Subject Passive l 2.65 1 1 3.30 2 2.42 l 2 2.00 3 3.30 l 3 0.09 4 0. 19 14 0.04 5 l .25 l 5 4.56 6 2.00 l 6 3.33 (continued) Subject Active Subject Passive 'T 3 .34 17 l .02 8 4.08 [3 0.39 9 0.70 l 9 2.78 10 2.89 20 1.65 a. Compute the tvalue and the p value by hand, then accept or reject the null hypothesis. b. Confirm your results on a computer. How does the computer output compare with your handcalculated results? Hint: In the computer database, create two columns. In column 1 (the grouping variable) enter the number 1 in rows 1 to 10 and the number 2 in rows 11 to 20. In column 2 (the score column), enter the absolute error values for subjects 1 to 10 in rows 1 to 10 and the values for subjects 11 to 20 in rows 11 to 20. 8. A sport psychologist wondered whether motivation could improve aerobic capacity. To answer the question, he measured 10 subjects on OZmax (ml/kg/min) on a treadmill. Students were verbally instructed to do their very best. One week later, the subjects were measured again and were told they would receive $100 if their 02max was higher than it was the rst time. Following are the data. First Second 45 54 33 50 59 5 B 32 3B 30 42 27 35 29 3B 59 66 44 4B 40 49 a. Did the money cause them to significantly increase their Ozmax values? b. If so, what is the probability of error in your conclusion? Should you accept or reject the null hypothesis? 0. Check your hand calculations on a computer. Hint: In the computer database, enter values for each subject on the same row. Use column 1 for the rst test and column 2 for the second test. 9. An aerobic dance teacher wanted to know whether two workouts per week of 30 minutes each were enough to increase Ozmax in sedentary middle-aged women. The teacher proposed to compare Ozmax of some women who had been in the aerobic dance classes for 6 months with Ozmax of a group of sedentary women. Based on related literature, the teacher estimated that OZrnax would be about 7 milliliters per kilogram per minute higher in the aerobic dancers, with a standard deviation of 4.5. If this is a fair estimate of the data to be expected, how many women must she test in each group to produce a power coefcient of .90 at or = .05? 5. A graduate student in biomechanics was interested in stride length of cross-country skiers. Stride length is an important factor in the development of speed for racing. Data were collected on 20 athletes from the cross-country ski team (the experimental group). The data were compared with those of a second group of 17 students (the control group) who were not varsity athletes but did participate in recreational skiing. The researcher assumed that no signicant differences would be found. Does a signicant difference in stride length exist between the athletes and the nonathletes? What is the level of condence? What is 032, and what is the ES (effect size)? (Adapted from Duoos, 1984; data fabricated.) Athletes Nonathleles 1?: = 0.90 meters f1 = 0.70 meters NI = 20 N2 : 17 SD] = 0.]? SD2 = 0.23 6. Find the 1' value for the following data on dominant versus nondominant grip strength. Twenty subjects were measured twice, once with the dominant hand and once again with the nondominant hand. Which hypothesis, H0 or H1, might be appropriate in this study? Is the difference signicant, and if so, at what level of condence? Domith Nondominant f. = 40 pounds 1?, = 35 pounds SDl = 12.7 r = .83 SD, = [4.2 7. A researcher in exercise physiology wanted to know Whether body composition differs among prepubescent males and females. To test the null hypothesis, she measured skinfolds (in millimeters) on 5 males and 6 females and obtained the following results. Males Females 2 l 22 25 19 19 l 8 17 24 [8 2 l 23 a. Is the difference in the means significant? If so, at what level of confidence? b. Do you accept or reject the null hypothesis? 0. Check your hand calculations on a computer. See the hint in problem 4