Problem 2

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Analytical Sciences Digital Library

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A preliminary analysis of the data from Problem 1 suggests that the pennies come from two populations, one clustered around a mass of 2.5 g and the other clustered around a mass of 3.1 g. A possible factor that might help in further analyzing this data is the age of the pennies. Open Data Set 2, which is an Excel file containing the masses and years of minting for the 32 pennies in Data Set 1.

Task 1. Characterize the data visually by creating a scatterplot with mass on the y-axis and the year of minting on the x-axis. Be sure to scale the axes so that the data occupy most of the available space. In several sentences, explain what information this graph conveys about the data. As part of your answer, be sure to include the terms population and sample, and to offer at least one plausible explanation for any trends you see in this data.

Task 2. Based on your results from Task 1, divide the data into two groups and determine the mean and standard deviation for each. You first might find it helpful to sort the data. Compare your estimate for the uncertainty in a penny's mass (Problem 1 - Task 4) to your calculated standard deviations. Do these comparisons support your conclusions from Task 1? Explain. Does dividing the pennies into two groups explain all the uncertainty in your data? Explain. If no, then suggest some other sources of uncertainty.

Task 3. Clearly there is an interesting trend to this data. How might you redesign this experiment to provide a more complete answer to the original question: What is the mass of a US penny?

After completing these tasks, proceed to Problem 3.