Calculate confidence intervals for ratio of two population variances and ratio of standard deviations. Assume that samples are simple random samples and taken from normal populations. a) alpha=0.05, n_{1}=30, s_{1}=16.37, n_{2}=39, s_{2}=9.88 b) alpha=0.01, n_{1}=25, s_{1}=5.2, n_{2}=20, s_{2}=6.8

djeljenike 2021-03-09 Answered
Calculate confidence intervals for ratio of two population variances and ratio of standard deviations. Assume that samples are simple random samples and 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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StrycharzT
Answered 2021-03-10 Author has 102 answers

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= (s12s22 F1  α2, n2  1, n1  1, s12s22Fα2, n2  1, n1  1)
CI= (16.3729.882 F1  0.052.39  1.30  1, 16.3729.882F0.52.39  1.30  1)
CI= (16.3729.882 F0.952, 38, 29, 16.3729.882F0.52, 38, 29) Using the critical value table, CI= (16.3729.882 ×0.507,  16.3729.8822.038)
CI= (1.3919, 5.5949) Hence, it is 95% confidence that the true ratio of population variances lies in interval (1.3919, 5.5949)

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= (s12s22 F1  α2, n2  1, n

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