Question

1. Coca-cola is testing a new processing line for filling 16-oz. bottles. They perform a test run in which 100 cases, each containing 24 bottles, are completed. From this test-run they randomly select 6 cases and take measurements on 5 randomly selected bottles from each case. Results for each of the six cases are shown in the table below. Estimate the average number of ounces per bottle and provide an appropriate error bound for your estimate.

Case	Average Fill for the 5 bottles tested	Sample variance for the five bottles tested
1	15.95	0.18
2	16.02	0.17
3	15.83	0.10
4	15.92	0.12
5	16.23	0.21
6	15.94	0.12

Answer 1

Total no of cases= 100

No of bottles in each case= 24

Total number of bottles or the total population= 2400

Sample for which the test was carried out = 6 cases

% of sample = 5x6/2400 = 30/2400= 1/80= 0.01

We tabulate the actual fill of the bottles by subtracting the variance from the data.

case	Actual fill of the bottles
1	15.77
2	15.85
3	15.73
4	15.8
5	16.02
6	15.82
Average fill =	15.83

Therefore the average ounces per bottle is 15.83 with error of 0.01%