Final answer:
The manufacturer's claim of having 20 rice cakes per package is not accurate as the sample mean is 17.75. However, the sample shows high precision as all package counts are consistently between 17 and 18 rice cakes.
Step-by-step explanation:
The accuracy and precision of the manufacturer's claim that there are 20 rice cakes per package can be assessed by looking at the sample of 12 packages with the counts provided. In this scenario:
- Accuracy refers to how close the sample mean is to the manufacturer's claimed value of 20 rice cakes.
- Precision refers to how consistent the counts are within the sample, irrespective of their mean.
To calculate the sample mean, we add all the counts together and divide by the number of packages:
Sample Mean = (18 + 17 + 17 + 17 + 18 + 18 + 18 + 17 + 18 + 17 + 18 + 17) / 12
Sample Mean = 213 / 12 = 17.75
This sample mean of 17.75 is lower than the claimed 20 rice cakes per package, indicating that the manufacturer's claim is not accurate based on this sample. As for precision, all package counts range between 17 and 18, which shows high consistency or precision in packaging. However, since the counts are all below the claimed value, the packaging process might be precisely inaccurate.