Question

Construct the confidence interval for the ratio of the population variances given the following sample statistics. Round your answers to four decimal places.

s₁²/s₂²=1.73, fα/2= 4.0646, f1−α/2= 0.3484
Lower endpoint___
Upper endpoint___

Answer 1

The confidence interval for the ratio of the population variances using the given sample variance ratio and critical values from the F-distribution is (0.6029, 7.0319) after rounding to four decimal places.

Step-by-step explanation:

To construct the confidence interval for the ratio of two population variances, we can use the sample variance ratio (s12/s22=1.73) and the critical values of the F-distribution (fα/2=4.0646 and f1-α/2=0.3484). The formula for the confidence interval is given by:

s12/s22 × (1/Fα/2, df1, df2) to s12/s22 × (F1-α/2, df1, df2), where df1 and df2 are the degrees of freedom for the two samples.

Applying the given values, we calculate the lower and upper endpoints of the confidence interval:

Lower endpoint = 1.73 × 0.3484 = 0.6029 (rounded to four decimal places)
Upper endpoint = 1.73 × 4.0646 = 7.0319 (rounded to four decimal places)

Therefore, the confidence interval for the ratio of the population variances is (0.6029, 7.0319).