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Solve the Problem σ21/σ22\sigma \frac { 2 } { 1 } / \sigma \frac { 2 } { 2 }

question 50

Multiple Choice

Solve the problem.
-A confidence interval estimate of the ratio σ21/σ22\sigma \frac { 2 } { 1 } / \sigma \frac { 2 } { 2 } can be found using the following expression:
(s12 s221 FR) <σ12σ22<(s12 s221 FL) \left(\frac{\mathrm{s}_{1}^{2}}{\mathrm{~s}_{2}^{2}} \cdot \frac{1}{\mathrm{~F}_{\mathrm{R}}}\right) <\frac{\sigma_{1}^{2}}{\sigma_{2}^{2}}<\left(\frac{\mathrm{s}_{1}^{2}}{\mathrm{~s}_{2}^{2}} \cdot \frac{1}{\mathrm{~F}_{\mathrm{L}}}\right)
where FR\mathrm { F } _ { \mathrm { R } } is found in the standard way and FL\mathrm { F } _ { \mathrm { L } } is found as follows: interchange the degrees of freedom, and then take the reciprocal of the resulting F value found in table A-5.
A manager at a bank is interested in the standard deviation of the waiting times when a single waiting line is us when individual lines are used. Obtain a 95%95 \% confidence interval for σ21/σ22\sigma \frac { 2 } { 1 } / \sigma \frac { 2 } { 2 } given the following sample data:
Sample 1: multiple waiting lines: n1=13, s1=2.1\mathrm { n } _ { 1 } = 13 , \mathrm {~s} _ { 1 } = 2.1 minutes
Sample 2: single waiting line: n2=16, s2=1.2\mathrm { n } _ { 2 } = 16 , \mathrm {~s} _ { 2 } = 1.2 minutes

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The demand or expectation from stakeholders to justify actions or decisions and take responsibility for outcomes.

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