Final answer:
The estimate of the common variance of the daily costs for the three delivery methods can be found using the formula for the variance of a sample. First, find the variance of each individual delivery method, then find the mean squared difference, and multiply it by the correction factor.
Step-by-step explanation:
The estimate of the common variance of the daily costs for the three delivery methods can be found using the formula for the variance of a sample. First, find the variance of each individual delivery method by subtracting the mean of each method from each data point, squaring the result, and then summing the squared differences.
Next, find the mean squared difference by dividing the sum of squared differences by the number of data points minus 1. Lastly, multiply the mean squared difference by the correction factor, which is the ratio of the number of data points to the total number of data points minus 1. The resulting value is the estimate of the common variance.
For example, let's say the daily costs for the three delivery methods are:
Method 1: 22, 25, 24, 21
Method 2: 19, 20, 18, 21
Method 3: 23, 20, 25, 24
First, calculate the variance for each method:
Method 1: ((22-23.0)^2 + (25-23.0)^2 + (24-23.0)^2 + (21-23.0)^2) / (4-1) = 3.33
Method 2: ((19-19.5)^2 + (20-19.5)^2 + (18-19.5)^2 + (21-19.5)^2) / (4-1) = 1.33
Method 3: ((23-23.0)^2 + (20-23.0)^2 + (25-23.0)^2 + (24-23.0)^2) / (4-1) = 3.33
Next, calculate the mean squared difference:
(3.33 + 1.33 + 3.33) / 3 = 2.33
Finally, multiply the mean squared difference by the correction factor:
2.33 * (4-1) / 4 = 1.75
Therefore, the estimate of the common variance of the daily costs for the three delivery methods is 1.75.