# 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

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) b)
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a) Given: Sample size, ${n}_{1}=30$ Sample size, ${n}_{2}=39$ Sample standard deviation 1, ${s}_{1}=16.37$ Sample standard deviation 2, ${s}_{2}=9.88$ Let's calculate $95\mathrm{%}$ confidence interval for the ratio of two population variances.

Using the critical value table,
Hence, it is $95\mathrm{%}$ confidence that the true ratio of population variances lies in interval

b) Given: Sample size, ${n}_{1}=25$ Sample size, ${n}_{2}=20$ Sample standard deviation 1, ${s}_{1}=5.2$ Sample standard deviation 2, ${s}_{2}=6.8$ Let's calculate $99\mathrm{%}$ confidence interval for the ratio of two population variances.