Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted and fuel wasted. Letx represent the average annual hours per person spent in traffic delays and lety represent the average annual gallons of fuel wasted per person in traffic delays. A random sample of eight cities showed the following data.
(b) Compute x and y for both sets of data pairs and compare the averages.
Compute the sample standard deviations
sx
and
sy
for both sets of data pairs and compare the standard deviations.
In which set are the standard deviations for
x and
y larger?
The standard deviations forx andy are larger for the first set of data.
The standard deviations forx andy
are larger for the second set of data. The standard deviations for
x andy are the same for both sets of data.
Look at the defining formula for
r. Why do smaller standard deviations
sx
and
sy
tend to increase the value of
r?
Dividing by smaller numbers results in a smaller value.
Multiplying by smaller numbers results in a larger value.
Multiplying by smaller numbers results in a smaller value.
Dividing by smaller numbers results in a larger value.
(c) Make a scatter diagram for the second set of data pairs.
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Verify that Σ
x = 173, Σ
x2 = 5205, Σ
y = 268, Σ
y2 = 13,518, and Σ
xy = 7851.
Compute
r.
(d) Compare
r from part (a) with
r from part (b). Do the data for averages have a higher correlation coefficient than the data for individual measurements?
No, the data for averages do not have a higher correlation coefficient than the data for individual measurements.
Yes, the data for averages have a higher correlation coefficient than the data for individual measurements.
List some reasons why you think hours lost per individual and fuel wasted per individual might vary more than the same quantities averaged over all the people in a city.