Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 9–3 Testing the Difference Between Two Means: Dependent Samples 501seminar. At a 0.10, did attending the seminarincrease the number of hours the students studiedper week?Before 9 12 6 15 3 18 10 13 7After 9 17 9 20 2 21 15 22 64. Obstacle Course Times An obstacle course wasset up on a campus, and 10 volunteers were given achance to complete it while they were being timed.They then sampled a new energy drink and were giventhe opportunity to run the course again. The “before”and “after” times in seconds are shown below. Is theresufficient evidence at a 0.05 to conclude that thestudents did better the second time? Discuss possiblereasons for your results.Student 1 2 3 4 5 6 7 8Before 67 72 80 70 78 82 69 75After 68 70 76 65 75 78 65 685. Sleep Report Students in a statistics class wereasked to report the number of hours they slept onweeknights and on weekends. At a 0.05, is theresufficient evidence that there is a difference in the meannumber of hours slept?Student 1 2 3 4 5 6 7 8Hours,Sun.–Thurs. 8 5.5 7.5 8 7 6 6 8Hours,Fri.–Sat. 4 7 10.5 12 11 9 6 96. PGA Golf Scores At a recent PGA tournament(the Honda Classic at Palm Beach Gardens, Florida)the following scores were posted for eight randomlyselected golfers for two consecutive days. At a 0.05,is there evidence of a difference in mean scores for thetwo days?Golfer 1 2 3 4 5 6 7 8Thursday 67 65 68 68 68 70 69 70Friday 68 70 69 71 72 69 70 70Source: Washington Observer-Reporter.7. Reducing Errors in Grammar A compositionteacher wishes to see whether a new grammar programwill reduce the number of grammatical errors herstudents make when writing a two-page essay. The dataare shown here. At a 0.025, can it be concluded thatthe number of errors has been reduced?Student 1 2 3 4 5 6Errors before 12 9 0 5 4 3Errors after 9 6 1 3 2 38. Overweight Dogs A veterinary nutritionistdeveloped a diet for overweight dogs. The totalvolume of food consumed remains the same, but onehalfof the dog food is replaced with a low-calorie“filler” such as canned green beans. Six overweightdogs were randomly selected from her practice andwere put on this program. Their initial weights wererecorded, and then they were weighed again after4 weeks. At the 0.05 level of significance can it beconcluded that the dogs lost weight?Before 42 53 48 65 40 52After 39 45 40 58 42 479. Pulse Rates of Identical Twins A researcherwanted to compare the pulse rates of identical twins tosee whether there was any difference. Eight sets of twinswere selected. The rates are given in the table as numberof beats per minute. At a 0.01, is there a significantdifference in the average pulse rates of twins? Find the99% confidence interval for the difference of the two.Use the P-value method.Twin A 87 92 78 83 88 90 84 93Twin B 83 95 79 83 86 93 80 8610. A random sample of six music students played ashort song, and the number of mistakes each studentmade was recorded. After they practiced the song5 times, the number of mistakes each student made wasrecorded. The data are shown. At a 0.05, can it beconcluded that there was a decrease in the mean numberof mistakes?Student A B C D E FBefore 10 6 8 8 13 8After 4 2 2 7 8 9Extending the Concepts11. Instead of finding the mean of the differences betweenX 1 and X 2 by subtracting X 1 X 2 , you can find it byfinding the means of X 1 and X 2 and then subtracting themeans. Show that these two procedures will yield thesame results.9–31