In: Statistics and Probability
You are given the following scores from two randomly drawn independent samples: X: 6,7,8,8,11 and Y: 3,4,4,7,7 a) state formally the hypothesis necessary to conduct a nondirectional test of no difference between the two population means. b) complete the test at the .05 and 0.01 levels of significance, and state your conclusions.
(a)
(b)
(i)
From the given data, the following statistics are calculated:
n1 = 5
s1 = 1.8708
n2 = 5
s2 = 1.8708
Test Statistic is given by:
t = (8 - 5)/1.1832
= 2.5355
ndf = 5 + 5 - 2 = 8
From Table, critical values of t = 2.3060
Since the calculated value of t = 2.5355 is greater than critical value of t = 2.3060, the difference is significant. Reject null hypothesis.
Conclusion:
The data do not support the claim that there is no difference between the two population means.
(ii)
From Table, critical values of t = 3.3554
Since the calculated value of t = 2.5355 is less than critical value of t = 3.3554, the difference is not significant. Fail to reject null hypothesis.
Conclusion:
The data support the claim that there is no difference between the two population means.