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Revision. Assume we have a group of 10 rats daily injected with 50 µg Pb /kg b. wt. At the end of experiment, the Pb concentrations in the liver and kidney were measured and tabulated as mean ± standard error in the following table:.

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  1. Revision Assume we have a group of 10 rats daily injected with 50 µg Pb/kg b. wt. At the end of experiment, the Pb concentrations in the liver and kidney were measured and tabulated as mean ± standard error in the following table: Is there any significant difference between the liver and kidneys in the levels of accumulated Pb at confidence level 95%?

  2. Solution: So we want to test the null hypothesis H0: σ22 = σ12 against the alternate hypothesis HA: σ22≠ σ12 (2-tailed) d.f.= 10 – 1 = 9 F0.025(9,9) = 4.03 In this case, Fcalc(17.78) > Ftabulated(4.03), so we reject H0that the two standard deviations are unequal,so P < 0.05

  3. Three diets (I, II, III) for mice were tested for differences in body weight (in grams) after a specified period of time. The results are recorded in the following table: Does the type of diet significantly affected the body weight of mice at confidence levels of 95% and 99 %? Compare between group I and II.

  4. Solution For I, σ2=25 For II, σ2=68.75 For III, σ2=63.75

  5. = 1316.66 dfB= h-1= 3-1= 2 MSB= SSB/dfB= 658.33

  6. = 472.5 dfW= N-h= 12-3= 9 MSW= SSW/dfW= 52.5

  7. F0.05 (2, 9)= 4.26 F0.01 (2, 9)= 8.02

  8. f-distribution Table

  9. Tukey’s HSD (Honestly significance difference) Post-hoc test Number of groups = number of means Total number of Samples The critical value for comparison between two averages Critical q value (tabulated) Sample size /group

  10. Tukey’s HSD (Honestly significance difference) Post-hoc test Q= 3.95 (3.62)=14.31 -= 7.5 <Q (14.31) insignificant

  11. N (total sample size)- g (number of groups) g (3) 12– 3= 9

  12. The data below represent the levels of blood glucose before and after injection with a certain herbal extract. Did the herbal extract cause increased blood glucose levels??

  13. d.f. = n - 1 ttabulated at d.f. 5 = 2.015 tCal(12.84) > ttabulated(2.015) Significant, P<0.05 =12.84

  14. In an experiment to study the effect of pH value on the hepatic Cd content, the data below were recorded. Test the claim that Cd content at pH 8 is significantly higher than at pH 5?

  15. d.f.= n1 + n2 - 2 = 7+11 -2= 16 =15.73 =12

  16. = = 1.001 ttabulated at d.f. (7+11-2) = 1.746 tCal (1.001) < ttabulated(1.746) Insignificant, P>0.05

  17. t-distribution Table

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