Chapter 53

Calculate and interpret standard errors. Two samples, \(A\) and \(B\), gave the following descriptive statistics (measured in the same units): Sample \(A\), mean \(=16.2\), standard deviation \(=12.7\), number of data values \(=12\); Sample B, mean \(=\) 13.2, standard deviation 14.4, number of data values \(=20\). Which has the lower standard error in absolute terms and in proportion to the sample mean? (Express answers to three significant figures.)

Compute a mean value correctly. A researcher finds that the mean vitamin concentration in three replicate samples designated \(A, B\) and \(C\) is \(3.0,2.5\) and \(2.0 \mathrm{mg}\), respectively. He computes the mean vitamin concentration as \(2.5 \mathrm{mg}\), but forgets that the sample sizes were 24,37 and 6, respectively. What is the true mean vitamin concentration? (Answer to three significant figures.)