An article in Fire Technology investigated two different foam expanding agents t
ID: 3134564 • Letter: A
Question
An article in Fire Technology investigated two different foam expanding agents that can be used in the nozzles of fire-fighting spray equipment. A random sample of five observations with an aqueous film-forming foam (AFFF) had a sample mean of 4.9 and a standard deviation of 0.65. A random sample of five observations with alcohol-type concentrates (ATC) had a sample mean of 6.9 and a standard deviation 0.80. Construct the following: A 90% two-sided confidence interval on sigma_1^2/sigma_2^2 A 95% two-sided confidence interval on sigma_1^2/sigma_2^2 Comment on the comparison of the width of this interval with the width of the interval in part (a). A 90% lower-confidence bound on sigma_1^2/sigma_2^2 The 90% two-sided confidence interval on sigma_1^2/sigma_2^2 is () Round your answers to three decimal places (e.g. 98.765). The 95% two-sided confidence interval on sigma_1^2/sigma_2^2 is () Round your answers to three decimal places (e.g. 98.765).Explanation / Answer
a).
90% CI =(0.103, 4.217)
b).
95% CI =(0.069, 6.340)
c).
90% lower bound = 0.161
Minitab used.
Out put for a).
Test and CI for Two Variances
Method
Null hypothesis (First) / (Second) = 1
Alternative hypothesis (First) / (Second) 1
Significance level = 0.05
F method was used. This method is accurate for normal data only.
Statistics
95% CI for
Sample N StDev Variance StDevs
First 5 0.650 0.423 (0.389, 1.868)
Second 5 0.800 0.640 (0.479, 2.299)
Ratio of standard deviations = 0.813
Ratio of variances = 0.660
95% Confidence Intervals
CI for
CI for StDev Variance
Method Ratio Ratio
F (0.262, 2.518) (0.069, 6.340)
Tests
Test
Method DF1 DF2 Statistic P-Value
F 4 4 0.66 0.697
Out put for b).
Test and CI for Two Variances
Method
Null hypothesis (First) / (Second) = 1
Alternative hypothesis (First) / (Second) 1
Significance level = 0.1
F method was used. This method is accurate for normal data only.
Statistics
90% CI for
Sample N StDev Variance StDevs
First 5 0.650 0.423 (0.422, 1.542)
Second 5 0.800 0.640 (0.519, 1.898)
Ratio of standard deviations = 0.813
Ratio of variances = 0.660
90% Confidence Intervals
CI for
CI for StDev Variance
Method Ratio Ratio
F (0.321, 2.054) (0.103, 4.217)
Tests
Test
Method DF1 DF2 Statistic P-Value
F 4 4 0.66 0.697
Out put for c).
Test and CI for Two Variances
Method
Null hypothesis (First) / (Second) = 1
Alternative hypothesis (First) / (Second) > 1
Significance level = 0.1
F method was used. This method is accurate for normal data only.
Statistics
90% Lower
Bound for
Sample N StDev Variance StDevs
First 5 0.650 0.423 0.466
Second 5 0.800 0.640 0.574
Ratio of standard deviations = 0.813
Ratio of variances = 0.660
90% One-Sided Confidence Intervals
Lower Bound Lower Bound
for StDev for Variance
Method Ratio Ratio
F 0.401 0.161
Tests
Test
Method DF1 DF2 Statistic P-Value
F 4 4 0.66 0.651
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