Question

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.

x (hr)	26	5	18	39	19	25	15	5
y (gal)	47	3	33	57	34	39	29	9

(a) Draw a scatter diagram for the data.

Verify that Σx = 152, Σx² = 3782, Σy = 251, Σy² = 10155, and Σxy = 6155.

Compute r.

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)	22	4	23	45	16	27	2	35
y (gal)	64	8	11	53	23	32	4	71

(b) Compute x and y for both sets of data pairs and compare the averages.

	x	y
Data 1
Data 2

Compute the sample standard deviations s_x and s_y for both sets of data pairs and compare the standard deviations.

	sx	sy
Data 1
Data 2

In which set are the standard deviations for x and y larger?

The standard deviations for x and y are larger for the first set of data.

The standard deviations for x and y are larger for the second set of data.    
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_x and s_y 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.

Verify that Σx = 174, Σx² = 5268, Σy = 266, Σy² = 13,700, and Σxy = 7803.

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.     

Answer 1

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b)

Data1	19	31.375
Data 2	21.75	33.25

	sx	sy
Data1	11.301	18.047
Data 2	14.558	26.337

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The standard deviations for x and y are larger for the second set of data.    

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Dividing by smaller numbers results in a larger value.

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d)  Yes, the data for averages have a higher correlation coefficient than the data for individual measurements.