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### Presentation1

1. 1. ANALYSIS OF VARIANCE ANOVA Presented by Love kush (2k81m49) Source :-www.indiastat.com
2. 2. Question :-1 Following data shows the fatal accidents occur in the factories in the past year 2001-2006 an officer want check that the average number of all the accident in all the states are equal or not for this he take a samples from the record at a 5% significance level. Assam 15 9 6 12 5 4 Bihar 31 5 6 6 4 5 Daman & Diu and Dadra & Nagar Haveli 4 2 6 2 5 9 National Capital Territory of Delhi 2 13 6 5 17 15 Goa 4 13 3 13 15 8
3. 3. H(O):µ(1) = µ(2) = µ(3) =µ(4) = µ(5) H(1):µ(1) ≠ µ(2) ≠ µ(3) ) ≠ µ(4) ≠ µ(5) Anova: Single Factor SUMMARY Groups Count Sum Average Variance Row 1 6 51 8.5 18.7 Row 2 6 57 9.5 111.5 Row 3 6 28 4.666667 7.066667 Row 4 6 58 9.666667 37.46667 Row 5 6 56 9.333333 25.86667 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 105.6667 4 26.41667 0.658441 0.626564 2.75871 Within Groups 1003 25 40.12 Total 1108.667 29
4. 4. <ul><li>Since F(calculated.) < F (critical.), do not reject H(0). Therefore, conclude that average number of accident in the states are equal </li></ul>0.685 2.758
5. 5. Question :- 2 Income tax Corporation of India want to check that the duties paid by the public sector oil company India are equal or not so officer three samples from data and check at 5%level of significance. Oil and Natural Gas Corporation (ONGC) 9364.48 9522.25 12287.67 9533.64 Hindustan Petroleum Chemical Limited (HPCL) 7586.78 7275.86 9924.72 7479.9 Bharat Petroleum Corporation Limited (BPCL) 5443.36 9942.02 11689.08 11190.97
6. 6. <ul><li>H(O):µ(1) = µ(2) = µ(3) </li></ul><ul><li>H(1):µ(1) ≠ µ(2) ≠ µ(3) ) </li></ul>Anova: Single Factor SUMMARY Groups Count Sum Average Variance Row 1 4 40708.04 10177.01 1985909 Row 2 4 32267.26 8066.815 1550775 Row 3 4 38265.43 9566.358 8095182 ANOVA Source of Variation SS Df MS F P-value F crit Between Groups 9432596 2 4716298 1.216391 0.340728 4.256495 Within Groups 34895597 9 3877289 Total 44328193 11
7. 7. <ul><li>Since F(calculated.) < F (critical.), do not reject H(0). Therefore, conclude that that the duties paid by the public sector oil company India are equal it depends upon their production </li></ul>1.21 4.25
8. 8. <ul><li>Question :-3 </li></ul><ul><li>Power corporation of India has decided to setup a new power plant in various states so on the basis The basis of the utilization of electricity in various states has to decide that he want to set up a new power plant in various states or not. </li></ul>Haryana 8470.46 8899.93 9597.74 10051.01 10534.76 11721.7 12915.72 13807.14 15426.11 16642.97 Himachal Pradesh 1961.44 2099.42 2188.05 2213.87 2351.86 2529.03 2736.92 2954.16 3568.67 4300.46 Jammu & Kashmir 2520.4 2798.42 2652.68 2867.45 2992.03 3325.2 3534.2 3877 4188.54 4030.85
9. 9. <ul><li>H(O):µ(1) = µ(2) = µ(3) </li></ul><ul><li>H(1):µ(1) ≠ µ(2) ≠ µ(3) </li></ul>Anova: Single Factor SUMMARY Groups Count Sum Average Variance Row 1 10 118067.5 11806.754 7876459.886 Row 2 10 26903.88 2690.388 548456.7619 Row 3 10 32786.77 3278.677 363093.2103 ANOVA Source of Variation SS Df MS F P-value F crit Between Groups 520607701 2 260303850.5 88.86102361 1.32644E-12 3.354131 Within Groups 79092088.73 27 2929336.62 Total 599699789.8 29
10. 10. <ul><li>Since F(calculated.) >F (critical.), reject H(0). Therefore, conclude that that the utilization of energy is more so power corporation has to decide new power plant in various states. </li></ul>88.86 3.354
11. 11. Thank you?