Question

1. An epidemiologist wished to compare two rabies vaccines. Subjects who had previously received rabies vaccine were divided in two groups. Group 1 received a booster does of type 1 vaccine, and Group 2 received a booster dose of type 2 vaccine. Antibody responses were recorded two weeks later. The means, standard deviations, and sample sizes for the two groups were as follows:

Group	n	(mean) x	s
1	10	4.5	2.5
2	9	2.5	2.0

The data come from normally distributed populations. Do these data indicate that there is a difference in the effectiveness of the two vaccine used for booster doses? Let the level of significance = 0.01

Answer 1

Answer Date: 05/11/2019 To test the hypothesis is that there is a difference in the effectiveness of the two vaccines used for booster doses at 1% significance level. The null and alternative hypothesis is, H, : Ilı = ll? H2:41 = 42 The t test-statistics is, First, compute the pooled variance then find the value of the t test-statistics. The pooled variance is, (ni - 1)s+(n2 - 1)s (n-1)+(n2 - 1) (10-1)×2.502 + (9-1) 22 (10-1)+(9-1) = 5.191

The t test-statistics is, +- (T1 - 12)-(4- ) (4.50 – 2.50)-0 5.191 5.191 V 10 9 = 1.910 The t test-statistics is 1.910. The t-critical value is, The sample size is small and two-tailed test. Look in the column headed a = 0.01 and the row headed in the t distribution table by using degree of freedom is,

d.f.=n +n2 - 2 = 10 + 9-2 =17 The t-critical value is - 2.898 and 2.898). Decision The statistical decision is that the t-test statistics which is 1.910 is less than t-critical value which is 2.898, so the null hypothesis is fails to reject at 1% level of significance. There is insufficient evidence to indicate that there is a difference in the effectiveness of the two vaccines used for booster doses. The result is not statistically significant.

Answer 2

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