Practice Sheet – 2 Samples and 1 Sample Matched Difference
(1) In order to test the breaking ability of two types of cars, a simple random of 64 cars of each type was tested to determine the distance in feet required to stop when traveling at 40 mph. The findings are shown below: Average distance for Car A = 118 ft with SD of 10.1 ft Average distance for Car B = 109 ft with SD of 9.33 ft Test at the 1% level as to whether the average distance for Car A is longer than that for Car B. (2) An educator assigns special activities in addition to regular work to an elementary class of 18 students to see if it will improve reading abilities. Another class of 20 students follows the same curriculum but does not have the special activities. A test is given to both classes at the end of 8 weeks. The first class with the special activities scored an average of 51.48 with SD of 11.01, and the second class without the special activities scored an average of 41.52 with SD of 17.15. Is the difference in the average scores significant? Test at the 1% level of significance. (3) A testing laboratory is testing the life of air conditioning compressors produced by two different companies. A random sample of 400 units was taken from company A, and its unit lasted an average of 110 months with SD of 60 months. A random sample of 100 units was taken from company B, and its unit lasted an average of 90 months with SD of 40 months. Is the compressor from company A significantly better than that of company B? Test at the 5% level. (4) Through random assignment of 200 volunteers with severe migraine headaches, two groups, A and B, are formed, consisting of 100 people each. A serum is given to group A but a placebo is given to group B; otherwise, the groups are treated identically. It is found that 75 subjects in group A and 65 subjects in group B experience relief within 48 hours. Can you say, at the 5% level of significance, that the serum is more effective than the placebo in providing relief within 48 hours? (5) Food Lion advertises that it has lower food prices than Winn Dixie. To test the claim, Wilson Consumer Testing Company took a random sample of 27 food items that were common to both stores and got the following: Food Lion AV = $1.56 SD = $.85 Winn Dixie AV = $1.53 SD = $.86 Differences (FL – WD) AV = $.03 SD = $.12
Do the data seem to substantiate the claim? Test at the 1% level.
(6) Each summer, Wake Forest has a 4-week program for pre-freshmen who are interested in medical careers. The federal government requires that we give the students a pretest and a posttest in mathematics. The following results were obtained in 1989 and 1990: 1989 Pre 29 35 37 39 40 43 43 Post 42 36 40 41 35 47 42 Pre 33 37 29 39 35 48 25 37 38 64 1990 Post 38 39 33 54 38 53 34 44 41 63
(i) Is there a significant difference between the pretest and the posttest scores in 1989? Test at the 1% level. (ii) Is there a significant difference between the pretest and the posttest scores in 1990? Test at the 1% level. (iii)Is the improvement between the pretest and the posttest scores in 1990 significantly better than the improvement between the pretest and the posttest scores in 1989? Test at the 1% level.
Solution Key for 2 Samples and 1 Sample Matched Difference
(1) 2 Samples: z 5.23 P 0% it seems as if the average distance for Car A is larger than that for Car B. (2) 2 Samples: z 2.17 P 1.5% it doesn’t seem that the difference is significant. (3) 2 Samples: z 4 P 0% it seems as if the compressors from company A last longer than those of company B. (4) 2 Samples: z 1.55 P 6% serum does not seem to be more effective. (5) 1 Sample Matched Difference: z 1.3 P 9.5% the difference does not seem to be significant. (6) (i) 1 Sample Matched Difference: t 1.16 with df = 6, 10% < P < 25% there doesn’t seem to be significant improvement (ii) 1 Sample Matched Difference: t 3.74 with df = 9, P < 0.5% the improvement seems to be significant. (iii) 2 Samples: t 1.10 with df = 15, 10% < P < 25% the improvement in 1990 does not seem to be significantly better than the improvement in 1989.