Question

Makers of generic drugs must show that they do not differ significantly from “reference” drugs that they imitate. One aspect in which drugs might differ is their extent of their absorption in the blood. Data were collected from two groups of subjects, one used generic drug and the other group used reference drug. The average absorption extent for Reference drug that applied to N1=78 subjects was X ?1 = 2065 with the standard deviation of S1= 881.8. The average absorption extent for generic drug that applied to N2=79 subject was X ?2 = 2085 with the standard deviation of S2=643.5. Do the drugs differ significantly in absorption? State HO and H1 and test the significance of the difference between generic and reference drugs at 95% level

Answer 1

H₀:

H₁:

The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

                            = (2065 - 2085)/sqrt((881.8)^2/78 + (643.5)^2/79)

                            = -0.16

DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + ((s2^2/n2)^2/(n2 - 1))

      = ((881.8)^2/78 + (643.5)^2/79)^2/(((881.8)^2/78)^2/77 + ((643.5)^2/79)^2/78)

      = 141

With 141 df and 95% confidence interval the critical values are t_{0.025, 141} = +/- 1.977

As the test statistic value lies between the critical values (-1.977 < -0.16 < 1.977), so the null hypothesis is not rejected.

So at 95% confidence interval there is not sufficient evidence to support that there is a significance difference between generic and reference drugs .