Answer to Question #206941 in Statistics and Probability for Parise Hemanth kum

Question

Two random samples are drawn from normal population are given below

Can we conclude that the two samples are drawn from the same

population? Test at 5% level of significance.

Sample I 17 27 18 25 27 29 13 17

Sample II 16 16 20 27 26 25 21

Answer 1

Using R

The samples are normally distributed so we may proceed with a standard t-test. The t-test also assumes that the variances are equal. Let’s test that, too, using the var.test( ) variance test.

The resulting p-value (p = 0.5208) suggests that we should not reject the H₀ (variances are not different). Therefore, we should conduct a t-test. We are now able to complete our t-test, adding the argument var.equal = TRUE.

From this, we find that two samples are drawn from the same population (p>0.05).