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Goodness of Fit Chi-Square Test

Goodness of Fit Chi-Square Test. Chi-Square Test. The Test for Goodness of Fit ascertains that a certain function F(x) is the Distribution Function of a distribution from which a sample x 1 , x 2 , …, x n has been taken.

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Goodness of Fit Chi-Square Test

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  1. Goodness of FitChi-Square Test

  2. Chi-Square Test • The Test for Goodness of Fit ascertains that a certain function F(x) is the Distribution Function of a distribution from which a sample x1, x2, …, xn has been taken. • It determines whether your experimentally observed results are consistent with your hypothesis.

  3. Related Terms • Hypothesis. Proposed explanation of an observed phenomenon • Observed Results.Observations made during the course of an experiment • Expected Results. What you expect to see based on your hypothesis (predictions) • Phenotypes. The observable traits

  4. X2 (Chi-square) Test • (o - e) = observed - expected • e = expected results • o = observed results

  5. Chi Square Table

  6. Example We cross a purple flowering plant with another white flowering plant. The result of this cross is 30 purple flowering plants and 14 white flowering plants. The expected Punnett square ratio is 3 purple to 1 white.

  7. Chi Square Table

  8. Chi-SquareTest

  9. Steps – Chi Square Test • Formulate Hypothesis • Write Observed and Expected Value • Calculate Chi-Square Value (х02) • Choose Significance Level and Degree of Freedom • Find Chi-Square Value (T - A10) • If х02 ≤ T, Accept Hypothesis • If х02 > T, Reject Hypothesis

  10. Problem 1 If 100 flips of a coin result in 30 heads and 70 tails, can we assert on 5% level that the coin is fair?

  11. Problem 3 What would be the smallest number of heads in Problem 1 (If 100 flips of a coin result in 30 heads and 70 tails, can we assert on 5% level that the coin is fair?) under which the hypothesis “Fair Coin” is still accepted?

  12. Problem 5 If in rolling a die 180 times we get 25, 31, 33, 27, 29, 35 Can we claim on 5% confidence level that the die is fair?

  13. Problem 7 Between 1pm and 2pm on five consecutive days (Monday through Friday) a certain service station has 92, 60, 66, 62 and 90 Customers, respectively. Test the hypothesis that the expected number of customers during that hours is the same on these days. (use α = 5%).

  14. Problem 9 In a sample of 100 patients having a certain disease 45 are men and 55 women. Does this support the claim that the disease is equally common among men and women? (Choose α = 5%).

  15. Problem 15 If it is known that 25% of certain steel rods produced by a standard process will break when subjected to a load of 500 lb. Can we claim that a new process yields the same breakage rate, if we find that in a sample of 80 rods produced by the new process, 27 rods broke, when subjected to that load (Use α = 5%).

  16. Problem 17 In a table of properly rounded function values, even and odd last decimals should appear about equally often. Test this for the 90 values of J1(x) in Table A1 in Appendix 5.

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