Final answer:
To determine if there is more variation in the first population than in the second, an F-test for the ratio of variances is used at the 0.01 significance level. The variance ratio is computed using the provided standard deviations, and this ratio is compared with the critical F-value to make a decision about the hypothesis.
Step-by-step explanation:
The question asks whether there is more variation in the first population compared to the second, based on their respective standard deviations, with a hypothesis test at the 0.01 significance level. To test the hypothesis H0: σ1^2 ≤ σ2^2 against H1: σ1^2 > σ2^2, we would use an F-test for the ratio of the two variances, where F = (s1^2 / s2^2).
Given the sample standard deviations, s1 = 12 and s2 = 7, and the sample sizes n1 = 5 and n2 = 7, we calculate F = (12^2 / 7^2). To make a decision, we compare the calculated F-value to the critical F-value from the F-distribution table with degree of freedom df1 = n1 - 1 and df2 = n2 - 1 at the 0.01 level of significance.
If the calculated F-value is greater than the critical F-value, we reject the null hypothesis and conclude that there is significant evidence that the variation in the first population is greater than in the second. If not, we fail to reject the null hypothesis, meaning we do not have enough evidence to conclude that there is more variation in the first population.