Question

Two medicines A and B against the headache are compared based on the time of absorption by the body: For the sample of drug A, x ̅_1=21.8 minutes,〖 s〗_1=8.7,〖 n〗_1=51 For the sample of drug B, x ̅_2=18.9 minutes,s_2=7.5,n_2=41 At the 5% significance level, is there a difference in absorption time between the two drugs if populations’ standard deviations are not equal. Given the critical value of t for 40 d.f. and 0.05 significance level (Two-tailed) is 2.021. Hint: H0 : 1 = 2 ; H1 : 1 ≠ 2

Answer 1

H₀:

H₁:

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

                             = (21.8 - 18.9)/sqrt((8.7)^2/51 + (7.5)^2/41)

                             = 1.72

Since the test statistic value is not greater than the upper critical value(1.72 < 2.021), so we should not reject the null hypothesis.

So at 5%bsignificance level, there is not enough evidence to conclude that there is a difference in absorption time between the two groups .