You are correct!
From the available data, it is impossible to say definitively whether Al’s statement is true or false. One way to look at this situation is to build a confidence interval with the data, around the mean of the sample, and see if 16 ounces is within these limits.
The sample mean is the best estimate for the number of ounces in each bottle. This is called a point estimate. Since there is variability in all systems, it is reasonable to expect that some bottles may have more than 16.1 and some less. What confidence does this response elicit, though? Typically, one would build a 99% or 95% confidence interval. With this data:
S = 3.1
n = 36
For a 95 percent level of confidence in the findings, the following formula can be used to calculate the confidence interval:
This means that one can be 95 percent confident that true mean will be somewhere between 15.09 and 17.101. Watch for further explanation next month. And don’t forget to watch the video.