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Chapter 1: Problem 90

In an attempt to determine any possible relationship between the year in which a U.S. penny was minted and its current mass (in grams), students weighed an assortment of pennies and obtained the following data. $$\begin{array}{lllllll}\hline 1968 & 1973 & 1977 & 1980 & 1982 & 1983 & 1985 \\\\\hline 3.11 & 3.14 & 3.13 & 3.12 & 3.12 & 2.51 & 2.54 \\\3.08 & 3.06 & 3.10 & 3.11 & 2.53 & 2.49 & 2.53 \\\3.09 & 3.07 & 3.06 & 3.08 & 2.54 & 2.47 & 2.53 \\\\\hline\end{array}$$ What valid conclusion(s) might they have drawn about the relationship between the masses of the pennies within a given year and from year to year?

Short Answer

Expert verified
After calculating and comparing the average masses, it becomes apparent that the mass of pennies decreased significantly after the year 1982. This observation provides a strong indication that there is a relationship between the U.S. pennies' current mass and their minting year. However, to precisely determine the nature of this relationship, a more detailed statistical analysis would be necessary.

Step by step solution

01

Identify Data Points

Observe the data provided regarding the mass of pennies from different years. Each row in the matrix corresponds to a set of data points from a series of years ranging from 1968 to 1985. The accompanying mass values for these years are given in grams.
02

Calculate the Average Mass

A sensible way to approach this data is to calculate the average mass of pennies for each year, which would provide a more concrete point for comparison. To do this, use the formula for the arithmetic mean, which is the sum of all values divided by the number of values. Calculate this for each year.
03

Compare Average Mass from Year to Year

After determining the average mass for pennies from each year, compare these averages. This will give an idea if there's an overall trend or particular pattern in the mass of pennies over the years.
04

Draw Conclusions

Based on the comparison of average masses, draw valid conclusions about the relationship between the year a penny was minted and its current mass. Also, observe any changes in the mass of pennies within a given year and from year to year.

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