Question

9. For each of the following calculated t-values and sample sizes, indicate the degrees of freedom and whether you should reject or not reject the null hypothesis (if you reject Ho, indicate whether it is at the .05 or .01 significance level). Conduct each of these t-tests using a two-tailed hypothesis. a. t = +2.18 ni = 5 n2 = 5 b. t= -2.05 n1 = 12 n2 = 10 c. t = -2.18 n = 15 n2 = 15 d. t = -2.05 n2 = 16 n2 = 16 10. Look at your four answers in question #9. What can you conclude about the relationship between sample size and rejecting the null hypothesis (i.e., is the t-test more powerful with smaller or with larger sample sizes).

Answer 1

This is an example of two sample t-test. The power of test depends on sample size. This is evident from the example below.

A . 9) For the given example . t-values and I sample sizes of two-sample t-test | The null nupothesis is Ho Mx = My vs H, : x 7 fly. The test statistic is T = x - y tnrn-2 n ng .d. f = n,+ na -2 , We reject Ho if Z ITI > tie an d. f tic (5%) Decision t (1%) Decision (5%) (1%) 2 .18 8 2.306 Accept.Mel 3.355 Accept He -2.05 | 20 2.086 Accept Hol 2.845 Accept Ho -2.18 | 28 | 2.048 Reject Holi 2.763 Accept Hot -2.05 | 30 | 2.042 e st Hal 2.750 | Accept Hot SI

1o) From answer of #9 we find that as the sample size increases the decision of rejecting the hypothesis increases. The t-test is more powerful as the sample size : increases, this is because the sampling distribution become narrower as soumple size increases. Which means there is less overlap of sampling distributions or null and alternative hypothesis.