In this "project" I will use the one-way Chi-square test to conduct a "preference study" to compare the preferences of 45 people among 3 "items." Question: Of these 3 choices, do you prefer Target, Costco, or Walmart? 45 answers: 1. Target 16. Costco 31. Target 2. Walmart 17. Target 32. Costco 3. Target 18. Walmart 33. Target 4. Costco 19. Costco 34. Costco 5. Target 20. Walmart 35. Walmart 6. Costco 21. Target 36. Costco 7. Walmart 22. Costco 37. Target 8. Target 23. Target 38. Walmart 9. Walmart 24. Costco 39. Target 10. Target 25. Walmart 40. Costco 11. Costco 26. Target 41. Walmart 12. Walmart 27. Walmart 42. Target 13. Costco 28. Target 43. Walmart 14. Walmart 29. Costco 44. Costco 15. Target 30. Walmart 45. WalmartTarget is Item 1 Costco is Item 2 Walmart is Item 3 1. What is the observed frequency (O) for Item 1? 2. What is the observed frequency (O) for Item 2? 3. What is the observed frequency (O) for Item 3? (Frequencies for questions 1. 2. & 3 should add up to 45.) 4. What is the expected frequency (E) for your items? 5. Using the formula below, what is your calculated value of Chi-square? x' = ) (0 - E) E 6. What is the null hypothesis for your study? (The null hypothesis is stated before you have any data so do not put your observed frequencies or your expected frequencies in your answer; the null hypothesis is often called symbolic or a statement---very much like 'innocent until proven guilty' is a court of law) 7. How many degrees of freedom do you have?8. Using Table 11 (Critical Values of Chi-Square) and the .05 level of significance, what is the critical value for this project? (Round off to 2 Decimal places) 9. Is the calculated value of Chi-square "statistically significant" or "statistically not significant"? 10. Did you "reject" or "fail to reject" the null hypothesis? Table 11 Critical Values of Chi-Square' .05 .01 001 05 .01 .001 df level level level df level level level 3.841 6.635 10.827 24 36.415 42.980 51.179 5.991 9.210 13.815 25 37.652 44.314 52.620 WN 7.815 11.345 16.268 26 38.885 45.642 54.052 9.488 13.277 18.465 27 40.113 46.963 55.476 u A 11.070 15.086 20.517 28 41.337 48.278 56.893 6 12.592 16.812 22.457 29 42.557 49.588 58.302 7 14.067 18.475 24.322 30 43.773 50.892 59.703 8 15.507 20.090 26.125 9 16.919 21.666 27.877 10 18.307 23.209 29.588 11 19.675 24.725 31.264 12 21.026 26.217 32.909 13 22.362 27.688 34.528 14 23.685 29.141 36.123 15 24.996 30.578 37.697 16 26.296 32.000 39.252 17 27.587 33.409 40.790 18 28.869 34.805 42.312 19 30.144 36.191 43.820 20 31.410 37.566 45.315 21 32.671 38.932 46.797 22 33.924 40.289 48.268 23 35.172 41.638 49.728