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)	27	5	19	36	21	22	18	5
y (gal)	45	3	31	56	33	36	26	9

(a) Draw a scatter diagram for the data.

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.
Verify that Σx = 153, Σx² = 3685, Σy = 239, Σy² = 9273, and Σxy = 5833.

Compute r=

x (hr)	23	4	20	42	17	29	2	39
y (gal)	61	8	12	53	25	30	4	72

(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

Answer 1

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I have used excel to verify the answer

function used =SUM(corresp. column)

x	y	xy	x2	y2
27	45	1215	729	2025
5	3	15	25	9
19	31	589	361	961
36	56	2016	1296	3136
21	33	693	441	1089
22	36	792	484	1296
18	26	468	324	676
5	9	45	25	81
153	239	5833	3685	9273	Sum

here n = 8

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b)

Data 1	19.125	29.875
Data 2	22	33.125

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Data 1	10.412	17.456
Data 2	14.599	25.870