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

Ernstfalld

Ernstfalld

Answered question

2021-02-09

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

Answer & Explanation

nitruraviX

nitruraviX

Skilled2021-02-10Added 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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