Solution Found!
Let S21 denote the sample variance for a random sample of
Chapter 7, Problem 36E(choose chapter or problem)
Let \(S_{1}^{2}\) denote the sample variance for a random sample of ten ln(LC50) values for copper and
let \(S_{2}^{2}\) denote the sample variance for a random sample of eight ln(LC50) values for lead, both
samples using the same species of fish. The population variance for measurements on copper is assumed to be twice the corresponding population variance for measurements on lead. Assume \(S_{1}^{2}\) to be independent of \(S_{2}^{2}\).
Find a number b such that
\(P\left(\frac{S_{1}^{2}}{s_{2}^{2}} \leq b\right)=.95\)
Find a number a such that
\(P\left(a \leq \frac{s_{1}^{2}}{s_{2}^{2}}\right)=.95\)
[Hint: Use the result of Exercise 7.29 and notice that \(\mathrm{P}\left(\mathrm{U}_{1} / \mathrm{U}_{2} \leq \mathrm{k}\right)=\mathrm{P}\left(\mathrm{U}_{2} / \mathrm{U}_{1} \geq 1 / \mathrm{k}\right)\).]
If a and b are as in parts (a) and (b), find
\(\mathrm{P}\left(a \leq \frac{s_{1}^{2}}{S_{2}^{2}} \leq b\right)=.95\)
Equation Transcription:
Text Transcription:
S_1^2
S_2^2
S_1^2
S_2^2
P(S_1^2 s_2^2 \leq =.95
P(a \leq s_1^2 s_2^2=.95
P(U1/U2 \leq k)=P(U2/U1\geq 1/k)
P(a \leq \s_1^2 S_2^2 \leq b =.95
Questions & Answers
QUESTION:
Let \(S_{1}^{2}\) denote the sample variance for a random sample of ten ln(LC50) values for copper and
let \(S_{2}^{2}\) denote the sample variance for a random sample of eight ln(LC50) values for lead, both
samples using the same species of fish. The population variance for measurements on copper is assumed to be twice the corresponding population variance for measurements on lead. Assume \(S_{1}^{2}\) to be independent of \(S_{2}^{2}\).
Find a number b such that
\(P\left(\frac{S_{1}^{2}}{s_{2}^{2}} \leq b\right)=.95\)
Find a number a such that
\(P\left(a \leq \frac{s_{1}^{2}}{s_{2}^{2}}\right)=.95\)
[Hint: Use the result of Exercise 7.29 and notice that \(\mathrm{P}\left(\mathrm{U}_{1} / \mathrm{U}_{2} \leq \mathrm{k}\right)=\mathrm{P}\left(\mathrm{U}_{2} / \mathrm{U}_{1} \geq 1 / \mathrm{k}\right)\).]
If a and b are as in parts (a) and (b), find
\(\mathrm{P}\left(a \leq \frac{s_{1}^{2}}{S_{2}^{2}} \leq b\right)=.95\)
Equation Transcription:
Text Transcription:
S_1^2
S_2^2
S_1^2
S_2^2
P(S_1^2 s_2^2 \leq =.95
P(a \leq s_1^2 s_2^2=.95
P(U1/U2 \leq k)=P(U2/U1\geq 1/k)
P(a \leq \s_1^2 S_2^2 \leq b =.95
ANSWER:Step 1 of 4
Given data
For n=10 samples of ln(LC50) values of copper
Sample variance is
For n=8 samples of ln(LC50) values of lead
Samples variance is
We are also given that