Question

A medical researcher is trying to determine whether the population variances of systolic blood pressure levels are the same for patients who take a new medication for high blood pressure and patients who do not take the new medication. The control group consists of 31 patients with a sample variance in systolic blood pressure of 165.120. The treatment group, who is taking the new medication, consists of 28 patients with a sample variance in systolic blood pressure of 85.010. Step 1 of 2 : Construct a 90% confidence interval for the ratio of the population variances of systolic blood pressure levels for the two groups. Find the lower and upper endpoints of the interval and round to four decimal places, if necessary.

Answer 1

To construct a confidence interval for the ratio of population variances, calculate the lower and upper endpoints using the F-distribution. In this case, the 90% confidence interval for the ratio of population variances is (0.3514, 0.7742).

Step-by-step explanation:

To construct a confidence interval for the ratio of population variances, we can use the F-distribution. Since we are comparing two groups with different sample sizes, we need to use the formula:

Lower Endpoint: [sample variance of treatment group / sample variance of control group] / F(nt-1), (nc-1)(1-α/2)

Upper Endpoint: [sample variance of treatment group / sample variance of control group] / F(nc-1), (nt-1)(1-α/2)

In this case, the sample variance of the control group is 165.120 and the sample variance of the treatment group is 85.010. The degrees of freedom are nc-1 = 31-1 = 30 and nt-1 = 28-1 = 27. Using the F-distribution table or a statistical software, we can find the critical F-value for a 90% confidence level, which is 1.555.

Substituting these values into the formula, we get:

Lower Endpoint: (85.010 / 165.120) / 1.555 = 0.3514

Upper Endpoint: (85.010 / 165.120) * 1.555 = 0.7742

Therefore, the 90% confidence interval for the ratio of population variances is (0.3514, 0.7742).