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 JJ-g) were measured. For pesticide A, the variance of the amounts absorbed in 6 specimens

Question

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?

Accepted Answer

Let [latex]σ^2_1[/latex] be the population variance for pesticide A, and let a [latex] σ^2_2[/latex] be the population variance for pesticide B. The null hypothesis is

[latex]H_0: \frac{\sigma_1^2}{\sigma_2^2}\leq 1[/latex]

The sample variances are [latex]s_1^2=2.3[/latex] and [latex]s_2^2=0.6[/latex]. The value of the test statistic is

[latex]F=\frac{2.3}{0.6}=3.83[/latex]

The null distribution of the test statistic is [latex]F_{5.9}[/latex]. If [latex]H_0[/latex] is true, then [latex]s^2_1[/latex] will on the average be smaller than [latex]s^2_2[/latex]. It follows that the larger the value of F, the stronger the evidence against [latex]H_0[/latex]. 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).

Question 7.9: In a series of experiments to determine the absorption rate ...

Related Answered Questions

Verified Answer:

In Example 7.9, σ²1 = 2.3 with a sample size of 6, and σ²2 = 0.6 with a sample size of 10. Test the null hypothesis H0: σ²1 = σ²2 ...

Verified Answer:

Refer to Example 7.7. Can you conclude that the mean number of items identified with the new structured design exceeds that of the conventional design by more than 2? ...

Verified Answer:

Good website design can make Web navigation easier. The article “The Implications of Visualization Ability and Structure Preview Design for Web Information Search Tasks” (H. Zhang and G. Salvendy, International Journal of Human-Computer Interaction, 2001 :75-95) presents a comparison of item ...

Verified Answer:

Verified Answer:

Verified Answer:

Refer to Example 7.2. Can you conclude that the mean diameter for carbon dioxide welds (μY) exceeds that for argon welds (μX) by more than 0.015 μm? ...

Verified Answer:

Verified Answer:

Verified Answer: