A pharmaceutical company is investigating the bioactivity of a new drug using 3

Question

A pharmaceutical company is investigating the bioactivity of a new drug using 3 different dosage levels. The results are: a) They wish to see if there is any evidence that the dosage level affects bioactivity, in order to evaluate this state the null and alternative hypotheses for the test. The result of the ANOVA using excel is shown below b) At a level of significance of alpha = .05, what is your conclusion? c) What is pooled standard deviation d) The author provided a rule to see if the requirement of equal standard deviations is met, what is the rule and is it satisfied?

Explanation / Answer

a) Null and alternate Hypothesis are Ho : 1 = 2 = 3 where s are the mean bioactivity for each of the 3 dosage levels Ha : Atleast one of the s is not equal to others b) = 0.05, From the ANOVA table we can see the p-value of the F-statistic is 4.43E-07 Thus p-value is less than . Hence we reject the null hypothesis Conclusion: There is statistically significant evidence which shows that the dosage level of the drug affects bioactivity c) Pooled Standard Deviation In ANOVA, the square root of the mean square error, pools the data from all samples to estimate the common Means Square (Error) = 17.666667 Pooled Standard Deviation = 17.66667 = 4.2032 Pooled Standard Deviation = 4.2032 d) Note to student : I am not aware what rule has been mentioned in your book. Hence providing a general rule which is used for testing equality of standard deviations. General rule is that if the largest sample Standard Deviation is not larger than twice the smallest sample Standard Deviation, we can assume equality of standard deviations In the given example. Largest Sample Standard Deviation = 5.076088 Smallest Sample Standard Deviation = 3.060501 2 x Smallest SD = 2 x 3.060501 = 6.1210 5.076088 < 6.1210 Hence the rule is satisfied

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