Question 7.9: In a series of experiments to determine the absorption rate ...
In a series of experiments to determine the absorption rate of certain pesticides into skin, measured amounts of two pesticides were applied to several skin specimens. After a time, the amounts absorbed (in μ-g) were measured. For pesticide A, the variance of the amounts absorbed in 6 specimens was 2.3, while for pesticide B, the variance of the amounts absorbed in 10 specimens was 0.6. Assume that for each pesticide, the amounts absorbed arc a simple random sample from a normal population. Can we conclude that the variance in the amount absorbed is greater for pesticide A than for pesticide B?
Let σ^2_1 be the population variance for pesticide A, and let a σ^2_2 be the population variance for pesticide B. The null hypothesis is
H_0: \frac{\sigma_1^2}{\sigma_2^2}\leq 1
The sample variances are s_1^2=2.3 and s_2^2=0.6. The value of the test statistic is
F=\frac{2.3}{0.6}=3.83
The null distribution of the test statistic is F_{5.9}. If H_0 is true, then s^2_1 will on the average be smaller than s^2_2. It follows that the larger the value of F, the stronger the evidence against H_0. Consulting the F table with five and nine degrees of freedom, we find that the upper 5% point is 3.48, while the upper 1% point is 6.06. We conclude that 0.01 < P < 0.05. There is reasonably strong evidence against the null hypothesis. See Figure 7.8 (page 306).
