Question

Construct the confidence interval for the ratio of the population variances given the following sample statistics. Round your answers to four decimal places. n1=18, n2=29, s₁²/s₂²=1.56, α=0.01.

Answer 1

To construct the confidence interval for the ratio of population variances, use the F-distribution formula with sample variances and degrees of freedom. Substitute the values and use the F-distribution table or calculator to find the confidence interval.

Step-by-step explanation:

To construct the confidence interval for the ratio of population variances, we can use the F-distribution. The formula is:

(s₁²/s₂²) * F(q₁, q₂, α/2) ≤ σ₁²/σ₂² ≤ (s₁²/s₂²) * F(1-q₁, 1-q₂, α/2)

where s₁² and s₂² are the sample variances, α is the significance level, and q₁ and q₂ are the degrees of freedom of the F-distribution. In this case, n₁ = 18, n₂ = 29, s₁²/s₂² = 1.56, and α = 0.01. Using the F-distribution table or calculator, we can find the values of F(q₁, q₂, α/2) and F(1-q₁, 1-q₂, α/2) and substitute them in the formula to calculate the confidence interval for the ratio of population variances.