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# qms Session 4.doc

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School
Department
Quantitative Methods
Course
QMS 102
Professor
Ron Babin
Semester
Summer

Description
Business Statistics II – QMS202 Dr. Changping Wang EXAMPLE : The Canada Revenue Agency reports that the average amount of income tax paid by Canadian individuals in 2010 is lower than \$10,000. A random sample of 20 individuals was randomly selected. Here are the amounts (in thousand dollars) of income tax paid in 2010 by those 20 people. 2, 3, 2.5, 5, 5, 3, 3.7, 0.9, 10, 11.5, 12, 28, 7.2, 11.3, 12.5, 0.5, 5.5, 9.3, 0.7, 0.9. Assume that the amount of income tax paid by Canadian individuals in 2010 is approximately normally distributed. Using a 0.01 level of significance, is there enough evidence to support the claim that the average amount of income tax paid by Canadian individuals in 2010 is lower than \$10,000? Winter 2012 – Session 4 Page 1 Business Statistics II – QMS202 Dr. Changping Wang 11.3 t Test of Hypothesis for the mean ( σ unknown) Winter 2012 – Session 4 Page 2 Business Statistics II – QMS202 Dr. Changping Wang Find critical value(s) using n-1 degree of freedom and the value(s) depend on the nature of the test. Winter 2012 – Session 4 Page 3 Business Statistics II – QMS202 Dr. Changping Wang Probability of exceeding the critical value 0.10 0.05 0.025 0.01 0.005 0.001 1. 3.078 6.314 12.706 31.821 63.657 318.313 2. 1.886 2.920 4.303 6.965 9.925 22.327 3. 1.638 2.353 3.182 4.541 5.841 10.215 4. 1.533 2.132 2.776 3.747 4.604 7.173 5. 1.476 2.015 2.571 3.365 4.032 5.893 6. 1.440 1.943 2.447 3.143 3.707 5.208 7. 1.415 1.895 2.365 2.998 3.499 4.782 8. 1.397 1.860 2.306 2.896 3.355 4.499 9. 1.383 1.833 2.262 2.821 3.250 4.296 10. 1.372 1.812 2.228 2.764 3.169 4.143 11. 1.363 1.796 2.201 2.718 3.106 4.024 12. 1.356 1.782 2.179 2.681 3.055 3.929 13. 1.350 1.771 2.160 2.650 3.012 3.852 14. 1.345 1.761 2.145 2.624 2.977 3.787 15. 1.341 1.753 2.131 2.602 2.947 3.733 16. 1.337 1.746 2.120 2.583 2.921 3.686 17. 1.333 1.740 2.110 2.567 2.898 3.646 18. 1.330 1.734 2.101 2.552 2.878 3.610 19. 1.328 1.729 2.093 2.539 2.861 3.579 20. 1.325 1.725 2.086 2.528 2.845 3.552 21. 1.323 1.721 2.080 2.518 2.831 3.527 22. 1.321 1.717 2.074 2.508 2.819 3.505 23. 1.319 1.714 2.069 2.500 2.807 3.485 24. 1.318 1.711 2.064 2.492 2.797 3.467 25. 1.316 1.708 2.060 2.485 2.787 3.450 26. 1.315 1.706 2.056 2.479 2.779 3.435 27. 1.314 1.703 2.052 2.473 2.771 3.421 28. 1.313 1.701 2.048 2.467 2.763 3.408 29. 1.311 1.699 2.045 2.462 2.756 3.396 30. 1.310 1.697 2.042 2.457 2.750 3.385 31. 1.309 1.696 2.040 2.453 2.744 3.375 32. 1.309 1.694 2.037 2.449 2.738 3.365 33. 1.308 1.692 2.035 2.445 2.733 3.356 34. 1.307 1.691 2.032 2.441 2.728 3.348 Probability of exceeding the critical value Winter 2012 – Session 4 Page 4 Business Statistics II – QMS202 Dr. Changping Wang 0.10 0.05 0.025 0.01 0.005 0.001 35. 1.306 1.690 2.030 2.438 2.724 3.340 36. 1.306 1.688 2.028 2.434 2.719 3.333 37. 1.305 1.687 2.026 2.431 2.715 3.326 38. 1.304 1.686 2.024 2.429 2.712 3.319 39. 1.304 1.685 2.023 2.426 2.708 3.313 40. 1.303 1.684 2.021 2.423 2.704 3.307 41. 1.303 1.683 2.020 2.421 2.701 3.301 42. 1.302 1.682 2.018 2.418 2.698 3.296 43. 1.302 1.681 2.017 2.416 2.695 3.291 44. 1.301 1.680 2.015 2.414 2.692 3.286 45. 1.301 1.679 2.014 2.412 2.690 3.281 46. 1.300 1.679 2.013 2.410 2.687 3.277 47. 1.300 1.678 2.012 2.408 2.685 3.273 48. 1.299 1.677 2.011 2.407 2.682 3.269 49. 1.299 1.677 2.010 2.405 2.680 3.265 50. 1.299 1.676 2.009 2.403 2.678 3.261 51. 1.298 1.675 2.008 2.402 2.676 3.258 52. 1.298 1.675 2.007 2.400 2.674 3.255 53. 1.298 1.674 2.006 2.399 2.672 3.251 54. 1.297 1.674 2.005 2.397 2.670 3.248 55. 1.297
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