Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted and fuel wasted. Let x represent the average annual hours per person spent in traffic delays and let y represent the average annual gallons of fuel wasted per per in traffic delays. A random sample of eight cities showed the following data. x (hr) 29 LY (gal) 49 22 38 32 55 15 25 3 34 39 Verify that Ex = 153, Ex? = 3805, Ey = 246, Ey? = 9842, and Exy = 6076. Compute r. (Round your answer to four decimal places.) The data in part (a) represent average annual hours lost per person and average annual gallons of fuel wasted per person in traffic delays. Suppose that instead of using average data for different cities, you selected one person at random from each city and measured the annual number of hours lost x for that person and the annual gallons of fuel wasted y for the same person. x (hr) 20 Ly (gal) 64 (b) Compute x and y for both sets of data pairs and compare the averages. (Round your answers to four decimal places.) 20 44 16 14 52 24 35 4 70 Data 1 Data 2 Compute the sample standard deviations s, and s, for both sets of data pairs and compare the standard deviations. (Round your answers to four decimal places.) Sx Sy Data 1 Data 2 In which set are the standard deviations for x and y larger? O The standard deviations for x and y are larger for the first set of data. O The standard deviations for x and y are larger for the second set of data. O The standard deviations for x and y are the same for both sets of data. Look at the defining formula for r. Why do smaller standard deviations s, and s, tend to increase the value of r? O Dividing by smaller numbers results in a larger value. O Multiplying by smaller numbers results in a larger value. O Multiplying by smaller numbers results in a smaller value. O Dividing by smaller numbers results in a smaller value.

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Description: Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted and fuel wasted. Let x represent the average annual hours per person spent in traffic delays and let y represent the average annual gallons of fuel wast

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.4: Combining And Decomposing Functions

Problem 8E

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Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted and fuel wasted. Let x represent the average annual hours per person spent in traffic delays and let y represent the average annual gallons of fuel wasted per person in traffic delays. A random sample of eight cities showed the following data.

I need help with
Look at the defining formula for r. Why do smaller standard deviations s_x and s_y tend to increase the value of r?

and (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?

And

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.

(c) Make a scatter diagram for the second set of data pairs.
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WebAssign. Graphing Tool
Verify that Ex = 169, Ex2 = 5057, Ey = 271, Ey? = 13,777, and Exy = 7772.
Compute r. (Round your answer to four decimal places.)
(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?
O No, the data for averages do not have a higher correlation coefficient than the data for individual measurements.
O 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.

Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted and fuel wasted. Let x represent the average annual hours per person spent in traffic delays and let y represent the average annual gallons of fuel wasted per per
in traffic delays. A random sample of eight cities showed the following data.
x (hr)
y (gal)
29
22
38
19
20
15
49
3
32
55
34
39
25
9
Verify that Ex = 153, Ex2 = 3805, Ey = 246, Ey? = 9842, and Exy = 6076.
Compute r. (Round your answer to four decimal places.)
The data in part (a) represent average annual hours lost per person and average annual gallons of fuel wasted per person in traffic delays. Suppose that instead of using average data for different cities, you selected one person at random from each city and
measured the annual number of hours lost x for that person and the annual gallons of fuel wasted y for the same person.
x (hr)
y (gal)
20
4
20
44
16
26
2
37
64
8
14
52
24
35
4
70
(b) Compute x and y for both sets of data pairs and compare the averages. (Round your answers to four decimal places.)
Data 1
Data 2
Compute the sample standard deviationss, and s,, for both sets of data pairs and compare the standard deviations. (Round your answers to four decimal places.)
Sx
Sy
Data 1
Data 2
In which set are the standard deviations for x and y larger?
O The standard deviations for x and y are larger for the first set of data.
O The standard deviations for x and y are larger for the second set of data.
O The standard deviations for x and y are the same for both sets of data.
Look at the defining formula for r. Why do smaller standard deviations s, and s, tend to increase the value of r?
O Dividing by smaller numbers results in a larger value.
O Multiplying by smaller numbers results in a larger value.
O Multiplying by smaller numbers results in a smaller value.
O Dividing by smaller numbers results in a smaller value.

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