A bottled water company bottles varying sizes of water, from 8-ounce to 1-gallon containers. The company has determined that the mean quantity in their 20-ounce bottles is 20.8 ounces with a standard deviation of 0.6 ounces. The bottling plant manager believes his machines are overfilling the bottles. A random sample of 30 bottles is taken, and the mean number of ounces of water is recorded. Which of the following values of the mean of the sample is most likely to occur if the true mean number of ounces is 20.8?
The mean of the sample means is the true population mean, 20.8 ounces. For a sample of 30 bottles, the standard error is 0.6 ÷ √30 ≈ 0.11 ounce, so sample means are most likely to be close to 20.8. Of the choices, 20.9 is closest, so it is the most likely sample mean.
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