Question 16 [4 marks] A sample of 100 employees from a company had their annual sales recorded. The results gave a mean salary of $19,500. From past experiences, it is known that the standard deviation of mean salaries is $2,500. Construct a 95% confidence interval for the true average salary of all employees. Question 17 (6 marks] Researchers compared an experimental drug with the standard drug for the treatment of a certain disease, 300 were given the experimental drug and 500 were given the standard drug. The number of patients who recovered from each group were recorded as follows Experimental Drug Standard drug Number of patients in Total 300 500 Number of recovered patients 225 371 Can we conclude, at the 10% level of significane, that the experimental drug had a higher proporion of recovered patients than the standard drug?below are all the formulas that were covered in the unit. In the final exam, if you use one of these formulas, please just write the formula number; for example, if you were performing a one-sample t- test for population mean, you would write "formula number 36". 1. 2. n N 3 [x-n(0) S = M-1 4. 0 = 5. 6. N-1 n-1 N-1 7. C. V. = or 8. XINT = Xx+f X (XX+1 - Xx) 9 IQR = Q3 - Q1 10. F Lmifi 11. S & [m'f-n() n-1 12. P (A) = n(A) M(AnB) n(5) 13. P(AnB) = "(AnB) 14. P(A B) = n (S) n(B) 15. P(A) = 1-P(A) 16. P(A UB) = P(A) +P (B) - P(AnB) 17. P (A VB) = P(A) + P (B) (Mutually exclusive events only) 18. P(AnB) = P(A) x P (B |A) 19. P (A n B) = P (A) XP (B) (Independent events only) 20. [ = E(X) = Ex . P (xi) 21. 62 = V(x) = E [x2 p(x)]- p2 22. p(x) = = n! *(m- P*(1 -p)-x 23. p(x) = My 24. EMV = Ex . p(x) 25. EVPI = EPPI - EMV* x! 26. 27. Xo = [+ z x G 28. 1 = A - M 29. P - P 30. 31. atta/, in 32. pa piza/T 33. n 2 34. n 2 -pa35. 36. P - P = 8 - P t= 8 - P 37. E = 39 Z=. -2)-(81- #2) 38. (x] - x2) i za/2 71 40. (1-Ix s + (n2-D)x 9; Mi+ n2-2 42. t = (4-37) -(21-42) 41. (x1 - x2) 1 ta/, Spent my 43. d + ta/, in 44. t = 3 = = ! (P1- P2) - (P1-P2) 45. 46. (p1 - p2) tz/ 47. x' = Zi=1- 48. x' = El Cj=1- 49. =(Ex - nx]) 50. , = ([y' - ny] ) 51. Say = (Exy - nip) 52. B1 = 53. Bo = y - BIX 54. S& = G. = SSerror n-2 55. SSerror = SSE = (n - 1) ; 56. Sry Sx X By 57. Bitto/,so, 58. t = P1 - B1 59. 1 =2 x 100 po 60. SAI = 281 x 100 61. L= [Pum * 100 62. P = [ Publi x 100 63. Real Price = Current Price x Base Year CPI Current Year CPITABLE 2 Critical Values of t d.f. to.1 to.05 to.025 to.01 to.005 d.f. to.1 to.05 to.025 to.01 to.005 3.078 6.314 12.706 31.821 63.657 36 1.306 1.688 2.028 2.434 2.719 1.886 2.920 4.303 6.965 9.925 37 1.305 1.687 2.026 2.431 2.715 3 1.638 2.353 3.182 4.541 5.841 38 1.304 1.686 2.024 2.429 2.712 4 1.533 2.132 2.776 3.747 4.604 39 1.304 1.685 2.023 2.426 2.708 5 1.476 2.015 2.571 3.365 4.032 40 1.303 1.684 2.021 2.423 2.704 6 1.440 1.943 2.447 3.143 3.707 41 1.303 1.683 2.020 2.421 2.701 1.415 1.895 2.365 2.998 3.499 42 1.302 1.682 2.018 2.418 2.698 1.397 1.860 2.306 2.896 3.355 43 1.302 1.681 2.017 2.416 2.695 9 1.383 1.833 2.262 2.821 3.250 44 1.301 1.680 2.015 2.414 2.692 10 1.372 1.812 2.228 2.764 3.169 45 1.301 1.679 2.014 2.412 2.690 11 1.363 1.796 2.201 2.718 3.106 46 1.300 1.679 2.013 2.410 2.687 12 1.356 1.782 2.179 2.681 3.055 47 1.300 1.678 2.012 2.408 2.685 13 1.350 1.771 2.160 2.650 3.012 48 1.299 1.677 2.011 2.407 2.682 14 1.345 1.761 2.145 2.624 2.977 49 1.299 1.677 2.010 2.405 2.680 15 1.341 1.753 2.131 2.602 2.947 50 1.299 1.676 2.009 2.403 2.678 16 1.337 1.746 2.120 2.583 2.921 51 1.298 1.675 2.008 2.402 2.676 17 1.333 1.740 2.110 2.567 2.898 52 1.298 1.675 2.007 2.400 2.674 18 1.330 1.734 2.101 2.552 2.878 53 1.298 1.674 2.006 2.399 2.672 19 1.328 1.729 2.093 2.539 2.861 54 1.297 1.674 2.005 2.397 2.670 20 1.325 1.725 2.086 2.528 2.845 55 1.297 1.673 2.004 2.396 2.668 21 1.323 1.721 2.080 2.518 2.831 56 1.297 1.673 2.003 2.395 2.667 22 1.321 1.717 2.074 2.508 2.819 57 1.297 1.672 2.002 2.394 2.665 23 1.319 1.714 2.069 2.500 2.807 58 1.296 2.002 2.392 2.663 24 1.318 1.711 2.064 2.492 2.797 59 1.296 1.671 2.001 2.391 2.662 25 1.316 1.708 2.060 2.485 2.787 60 1.296 1.671 2.000 2.390 2.660 26 1.315 1.706 2.056 2.479 2.779 27 1.314 1.703 2.052 2.473 2.771 70 1.294 1.667 1.994 2.381 2.648 28 1.313 1.701 2.048 2.467 2.763 80 1.292 1.664 1.990 0 2.374 2.639 29 1.311 1.699 2.045 2.462 2.756 90 1.291 1.662 1.987 7 2.368 2.632 30 1.310 1.697 2.042 2.457 2.750 100 1.290 1.660 1.984 2.364 2.626 31 1.309 1.696 2.040 2.453 2.744 32 1.309 1.694 2.037 2.449 2.738 150 1.287 1.655 1.976 2.351 2.609 33 1.308 1.692 2.035 2.445 2.733 200 1.286 1.653 1.972 2.345 2.601 34 1.307 1.691 2.032 2.441 2.728 35 1.306 1.690 2.030 2.438 2.724 1.282 1.645 1.960 2.326 2.576