Using Data for a Large Sample of Cars (N = $n = 93$

question 11

Essay

Using data for a large sample of cars (n = 93), a statistics student calculated a matrix of correlation coefficients for selected variables describing each car. (a) In the spaces provided, write the two-tailed critical values of the correlation coefficient for α = .05 and α = .01 respectively. Show how you derived these critical values. (b) Mark with * all correlations that are significant at α = .05, and mark with ** those that are significant at α = .01. (c) Why might you expect a negative correlation between Weight and HwyMPG? (d) Why might you expect a positive correlation between HPMax and Length? Explain your reasoning. (e) Why is the matrix empty above the diagonal?
Correlation Matrix ( $n = 93$ cars)

$\begin{array}{|c|c|c|c|c|c|c|}\text { MidPr}&\text { CityMPG}&\text { HwyMPG}&\text { EngSize}&\text { HPMax}&\text {Length}& \text {Weight }\\\hline \text { MidPr}&1.000 & & & & & & \\\hline\text { CityMPG}&-0.595 & 1.000 & & & & & \\\hline\text { HwyMPG}&-0.561 & 0.944 & 1.000 & & & & \\\hline\text { EngSize}&0.597 & -0.710 & -0.627 & 1.000 & & & \\\hline \text { HPMax}&0.788 & -0.673 & -0.619 & 0.732 & 1.000 & & \\\hline \text {Length}& 0.504 & -0.666 & -0.543 & 0.780 & 0.551 & 1.000 & \\\hline \text {Weight }&0.647 & -0.843 & -0.811 & 0.845 & 0.739 & 0.806 & 1.000 \\\hline\end{array}$



MidPr = midrange price (in $\$ 1,000 )$ - average of min and max prices
CityMPG = city MPG (miles per gallon by EPA rating)
HwyMPG highway MPG
EngSize = engine size (liters)
HPMax = horsepower (maximum)
Length $=$ length (inches)
Weight = weight (pounds)
Critical value for $.05$
Critical value for .01

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Definitions:

Solar Cells

Instruments that directly transform sunlight into electrical energy via the photovoltaic effect.

Carbon Dioxide

This substance is a transparent, unscented gas generated through the combustion of carbon and organic materials as well as through respiration, and it is a naturally occurring part of the atmosphere absorbed by plants for photosynthesis.

Solar Space Heating

The use of solar energy to heat the interior of a building, reducing the reliance on traditional heating sources.

Carbon Dioxide

A colorless, odorless gas produced by burning carbon and organic compounds and by respiration, a greenhouse gas contributing to global warming.