Question

Does a statistics course improve a student's mathematics skills, as measured by a national test? Suppose a random sample of 13 students takes the same national mathematics exam prior to enrolling in a stats course and just after completing the course. At a 1% level of significance determine whether the scores after the stats course are significantly higher than the scores before. Take the differences = before - after. Before 430 485 520 360 440 500 425 470 515 430 450 495 540 After 465 475 535 410 425 505 450 480 520 430 460 500 530 What type of alternative hypothesis is appropriate for this research question? O two-sided O one-sided Locate student in the dataset. What rank will be given to this student? What is the value of the test statistic, T? Give answer to 1 decimal place. What is the critical value for the study? (Hint: student 10 will be dropped from the analysis, since the scores are the same before and after the stats class). Are the exam scores significantly higher after the stats course? Yes O No

Answer 1

sl.no 12 6.5 9.5 13 9.5 difference = absolute before after before-after difference rank 1 430 465 -35 35 2 485 475 10 10 3 520 535 -15 15 4 360 410 -50 50 5 440 425 15 15 6 500 505 -5 5 7 425 450 -25 25 8 470 480 -10 10 9 515 520 -5 5 10 430 430 0 0 11 450 460 10 10 12 495 500 -5 5 3 11 6.5 CY 1 1 6.5 3 6.5 13 540 530 10 10

absolute difference rank sl.no difference = brand A- brand A brand B brand B 24 26 27 27 0 19 22 -3 1 41 5.5 T-= 1 T+ = 0 3 N 3 3 4 24 27 -3 3 8 T = 3 CO DO 5 22 25 -3 3 LD 26 27 1 7 27 26 -1 1 -2 1 3 8 25 27 2 5.5 9 22 23

Critical Values of the Wilcoxon Signed Ranks Test n Two-Tailed Test a = .05 a = .01 5 0 1 1 ذرا 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 2 3 5 8 10 13 17 21 25 29 34 40 46 52 58 65 73 81 89 98 107 116 126 137 5 7 9 12 15 19 23 27 32 37 42 48 54 61 68 75 83 91 100 109 One-Tailed Test a = .05 a= .01 0 2 3 0 5 8 3 10 5 13 7 17 9 21 12 25 15 30 19 35 23 41 27 47 32 53 37 60 43 67 49 75 55 83 62 91 69 100 76 110 84 119 92 130 101 140 110 151 120

b Ho: Mo: Bedore Matter Hi. M Betore Master a th alternative hypothesis One-Sided test Student rank will be Test statistic T = Min (T+ ,T) = 122.5 P[T+=22-5, T = 67.5] Critical value for 2=0.01&h=13 is T* = 12 C = 12 Cone-Tailed test) POIN (T = 22.5) 3 (7* = 12 ni rawan Teststatistic greater than Critical value. N 4.X Ca C 0 11 we do not Reject Hoa roggu The exam scones significantly higher after the stats course. Yes. 2) value of T = (Min (41,3)=13 [] =46), T+=3

M BrandB HoiM Brand A HIM Brand A & M Brand B (Two tailed test) Critical value for a=0.05 and n=9 is 7 * = 5 (T=3) < 1* = 5) . We reject Ho There is a significant diffenersie in the median ratings between the two coeffee brands