Question

help with the following f tests, thanks

A liposome suspension can degrade over time due to oxidation of the lipids in the membrane. Usually this results in fusion of the vesicles to form larger ones. A liposome suspension was measured when it was freshly made and checked a few months later. Has this sample degraded? Samplen Mean Diameter Standard Deviation Feb. 2012 3 1.33 * 102 nm 0.15 x 102 nm June 2012 3 1.42* 102 nm 0.19 * 102 nm Ftable for n=3, n=3: 19.0 ttable, 95% for d.f.=4: 2.776 A: Yes, they have changed size B: No, they have not changed size

Answer 1

	1	2
s	15	18
variance	225	324

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:o = ož Ha : 0=o This corresponds to a two-tailed test, for which a F-test for two population variances needs to be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the the rejection region for this two-tailed test is R= {F:F< 0.026 or F > 39}. (3) Test Statistics The F-statistic is computed as follows: F = = 325 = 0.694 (4) Decision about the null hypothesis Since from the sample information we get that FL = 0.026 <F = 0.694 < Fu = 39, it is then concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population variance oi is different than the population variance os, at the a = 0.05 significance level.

We fail to reject the null hypothesis

hence equal variance can be assumed

we will use 2A to calculate the t-test