The last digits of sample data are sometimes used in an attempt to determine whether the data have been measured or simply reported by the subject. Reported data often have last digits with disproportionately more 0's and 5's. Measured data tend to have last digits with a mean of 4.5, a standard deviation of about 3, and the digits should occur with roughly the same frequency.
a. How is the standard deviation of the data affected if there are disproportionately more 0's and 5's?
b. Why can we not use the methods of this section to test that the last digits of the sample data have a standard deviation equal to 3?