**Traffic Delay Data Analysis****Introduction:**Roadway congestion is a costly issue, both in terms of time wasted and fuel wasted. In this analysis, we let \( x \) represent the average annual hours per person spent in traffic delays, and \( y \) represent the average annual gallons of fuel wasted per person in traffic delays. A random sample of data from eight cities is provided below.**Data Sample (Part a):**| \( x \) (hr) | 29 | 5 | 18 | 39 | 22 | 21 | 15 | 5 ||--------------|----|---|----|----|----|----|----|--|| \( y \) (gal) | 48 | 3 | 35 | 57 | 31 | 37 | 25 | 9 |**Given:**- \( \Sigma x = 154 \)- \( \Sigma x^2 = 3886 \)- \( \Sigma y = 245 \)- \( \Sigma y^2 = 9823 \)- \( \Sigma xy = 6139 \)**Task:**Compute the correlation coefficient \( r \) and round the answer to four decimal places.**Data (Part b):**Instead of using average data for cities, data from individual persons in different cities were collected.| \( x \) (hr) | 21 | 4 | 22 | 44 | 17 | 25 | 2 | 38 ||--------------|----|---|----|----|----|----|----|--|| \( y \) (gal) | 61 | 8 | 15 | 52 | 25 | 32 | 4 | 71 |**Tasks:**1. **Compute Averages:** - Calculate the mean \(\bar{x}\) and \(\bar{y}\) for both sets of data pairs. - Compare these averages. - Round answers to four decimal places.2. **Compute Standard Deviations:** - Calculate the sample standard deviations \( s_x \) and \( s_y \) for both sets of data pairs. - Compare these standard deviations. - Round answers to four decimal places.**Note:** The computations and comparisons will help us understand the variation and relationship between time spent in traffic and fuel wasted across different contexts (average data vs.

Let x represent the average annual hours per person spent in traffic delays and y represent the average annual gallons of fuel wasted per person in traffic delays. And the data is given for eight cities , n = 8. It is asked to verify Σx = 154 , Σx² = 3886 , Σy=245 , Σy²=9823 , Σxy = 6139. Compute the value of correlation coefficient (r). Let's prepare a table to verify the above given values. Thus , we can say that the above given values are correct. Let's start to find correlation , r now. The formula to find correlation , r is as follows; r = n(Σxy)-(Σx)(Σy)[nΣx² - (Σx)²]×[nΣy²-(Σy)²] Here we know all the values so just plug and calculate r. r = 8(6139)-(154×245)[8(3886) - (154)²]×[8(9823)-(245)²]=113827372×18559=1138211696.878=0.9731 Thus , the value of correlation , r = 0.9731.Data set 2 : Now it is given that , the data in part (a) represent average annual hours lost per person and average annual gallons or fuel wasted per person in traffic delays. suppose that instead of using average data for different cities ones, you selected one person at random from each city and measured. Here x be the annual number of hours lost for that person and y be the annual gallons of fuel wasted y for the same person. The data set for this is given as follows; It is asked to Compute x and y for both sets of data pairs and compare the averages. Compute the sample standard deviations and for both sets of data pairs and compare the standard deviations. Let's calculate x and y for data set 1 : Data set 1 : Here we know that , Σx = 154 , Σy = 245. The formula's to find x and y are as follows; x = Σxn=1548=19.25y = Σyn=2458=30.625 For data set x and y are 19.25 and 30.625. Data set 2 : Data set 2 is as follows; The formula's to find x and y are as follows; x =Σxin = 21+4+22+44+17+25+2+388=1738=21.625.y =Σyin = 61+8+15+52+25+32+4+718=2688=33.5. For data set x and y are 21.625 and 33.5. Hence , x and y for both the data set's are as follows; From the above table , We can say that , Data set 2 values for x and y are larger than Data set 1. That is , Data set 2 > Data set 1.You can easily find sample standard deviation by using MS_EXCEL. The function to find standard deviation in excel is =STDEV(data1 , data2 , ....data8). For x , sample standard deviation , , sx = 11.4736. Similarly find sample standard deviation for y. So for y , sample standard deviation , sy = 18.2047. For data set 1 : sx = 11.4736 and sy = 18.2047.The function to find standard deviation in excel is =STDEV(data1 , data2 , ....data8). For x , sample standard deviation , sx = 14.6281. So for y , sample standard deviation , sy = 25.1907. For data set 2: sx = 14.6281 and sy = 25.1907The sample standard deviation for data 1 and data 2 are, Here also , Data set 2 values for sx and sy are larger than Data set 1. That is , Data set 2 > Data set 1.