Question

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.

Answer 1

(a)

H0: Null Hypothesis:

HA: Alternative Hypothesis:

(b)

(i)

For =0.05

From the given data, the following statistics are calculated:

n1 = 5

1 = 8

s1 = 1.8708

n2 = 5

2 = 5

s2 = 1.8708

Test Statistic is given by:

t = (8 - 5)/1.1832

= 2.5355

ndf = 5 + 5 - 2 = 8

= 0.05

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)

For = 0.01

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.