Question

A new method of determining oxyphen butazone gave 99.35% recovery (variance 0.185).The standard method gave 99.53% recovery (variance 0.152).In each case three replicate measurements were made. Test whether the two means differ significantly at the 95% confidence level.

Answer 1

Pooled Standard Deviation is given by:

$s_{P}=\sqrt{\frac{(n1-1)s1^{2}+(n2-1)s2^{2}}{n1+n2-2}}$

$=\sqrt{\frac{(3-1)\times 0.185+(3-1)\times 0.152}{3+3-2}}=0.4105$

Test Statistic is given by:

$t=\frac{0.9935-0.9953}{0.4105\sqrt{1/3+1/3}}=-0.0054$

$\alpha$ = 0.05

ndf = n1 + n2 - 2 = 3 + 3 - 2 = 4

From Table, critical values of t = $\pm$ 2.7764

Since calculated value of t = - 0.0054 is greater than critical value of t = - 2.7764, the difference is not significant. Reject null hypothesis.

Conclusion:
The data do not support the claim that the two means differ significantly at the 95% confidence level.