[EX08-040] The atomic weight of a reference sample of silver was measured at the National Institute of Standards and Technology (NIST) using two nearly identical mass spectrometers. This project was undertaken in conjunction with the redetermination of the Faraday constant. Following are 48 observations:

107.8681568 107.8681465 107.8681572

••• Remainder of data on Student’s Suite CD-ROM Source: StatLib, http://lib.stat.cmu.edu/datasets/

Notice that the data differ only in the fifth, sixth, and seventh decimal places. Most computers will round the data and their calculated results;

thus, the variation is seemingly lost. The statistics can be computed using just the last three digits of each data value (i.e., 107.8681568 will become 568). Algebraically this coding looks like this:

Atom Wt Coded  (Atomic weight  107.8681000) 10,000,000.

The data are listed in both the original and coded formats on the Student Suite CD.

a. Construct a graph of the coded data. How does the coding show on the graph?

b. Find the mean and standard deviation of the coded data.

c. Convert the answers found in part b to original units.

d. Determine whether the data has an approximately normal distribution. Present your case.

e. Do the SDSM and CLT apply? Explain.

f. Is sigma known?
g. If the goal is to find the 95% confidence interval for the mean value of all observations, what would you do?
h. Find the 95% confidence interval for the mean value of all such observations. Justify your method.