Answered: Fuming because you are stuck in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

x (hr)	27	5	23	39	20	20	17	5
y (gal)	46	3	34	54	34	39	29	9

Verify that Σx = 156, Σx² = 3918, Σy = 248, Σy² = 9796, and Σxy = 6143.

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)	23	4	22	40	16	29	2	36
y (gal)	64	8	14	51	23	30	4	74

(b) Compute x and y for both sets of data pairs and compare the averages. (Round your answers to four decimal places.)

Compute the sample standard deviations s_x and s_y for both sets of data pairs and compare the standard deviations. (Round your answers to four decimal places.)

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

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

(B)The standard deviations for x and y are larger for the second set 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?

(A) Multiplying by smaller numbers results in a smaller value.

(B)Multiplying by smaller numbers results in a larger value.

(C)Dividing by smaller numbers results in a larger value.

(D)Dividing by smaller numbers results in a smaller value.

Verify that Σx = 172, Σx² = 5026, Σy = 268, Σy² = 13,878, and Σxy = 7762.

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?

(A)No, the data for averages do not have a higher correlation coefficient than the data for individual measurements.

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

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