A new bottling machine is being tested by a company. During a test run, the machine fills 24 cases, each containing 12 bottles. The company wishes to estimate the average number of ounces of fill per bottle. A two stage cluster sample is employed using 6 cases(clusters), with 4 bottles (elements) randomly selected from each. The results are given in the accompanying table. Estimate the average number of ounces per bottle and find the variance of the estimate.

Case Avg ounces for sample ybar i sample variance s_{i}^{2}
1 7.9 0.15
2 8.0 0.12
3 7.8 0.09
4 7.9 0.11
5 8.1 010
6 7.9 0.12