Calculate the confidence intervals for the ratio of the two population variances and the ratio of standard deviations. Suppose the samples are simple

Ernstfalld 2021-02-09 Answered
Calculate the confidence intervals for the ratio of the two population variances and the ratio of standard deviations. Suppose the samples are simple random samples taken from normal populations.
a. α=0.05,n1=30,s1=16.37,n2=39,s2=9.88,
b. α=0.01,n1=25,s1=5.2,n2=20,s2=6.8
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nitruraviX
Answered 2021-02-10 Author has 101 answers
Step 1
a)
Given:
Sample size, n1=30
Sample size, n2=39
Sample standard deviation 1, s1=16.37
Sample standard deviation 2, s2=9.88
Let's calculate 95% confidence interval for the ratio of two population variances.
CI=(s12s22F1α/2,n21,n11,s12s22Fα/2,n21,n11)
CI=(16.3729.882F10.05/2,391,301,16.3729.882F0.05/2,391,301)
CI=(16.3729.882F0.95/2,38,29,16.3729.882F0.05/2,38,29)
Using the critical value table,
CI=(16.3729.882×0.507,16.3729.8822.038)
CI=(1.3919,5.5949)
Thus, it is 95% confidence that the true ratio of population variances lies in the interval (1.3919, 5.5949).
Step 2
b) Given:
Sample size, n1=25
Sample size, n2=20
Sample standard deviation 1, s1=5.2
Sample standard deviation 2, s2=6.8
Let's calculate 99% confidence interval for the ratio of two population variances.
CI=(s12s22F1α/2,n21,n11,s12s22Fα/2,n21,n11)
CI=(5.226.82F10.01/2,391,301,5.226.82F0.01/2,391,301)

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