3 **Title: Analyzing the Relationship Between Speed Limits and Automobile Accident Death Rates**---**Objective:**Consider the following analysis of speed limits and death rates from automobile accidents in selected countries.**Tasks:**a. **Construct a Scatter Diagram:** - Create a scatter plot to visually represent the data showing the relationship between speed limits and death rates. (Please place your scatter plot at the end of your answer sheet.)b. **Calculate the Correlation Coefficient:** - Determine the correlation coefficient (r) to understand the strength and direction of the relationship between speed limits and death rates. - Ensure the value of r is rounded to two decimal places.**Data Table:**- **Country:** Indexed from 1 to 10.- **Death Rate (per 100 million vehicle-miles):** - Country 1: 3.1 - Country 2: 3.4 - Country 3: 3.5 - Country 4: 3.6 - Country 5: 4.2 - Country 6: 4.4 - Country 7: 4.8 - Country 8: 5.0 - Country 9: 5.2 - Country 10: 6.2- **Speed Limit (miles per hour):** - Country 1: 54 - Country 2: 54 - Country 3: 54 - Country 4: 69 - Country 5: 54 - Country 6: 59 - Country 7: 54 - Country 8: 64 - Country 9: 59 - Country 10: 74**Analysis Notes:**- Use this data to explore how changes in speed limits might correlate with variations in death rates from automobile accidents. - Construct and interpret the scatter plot and correlation coefficient to draw conclusions about the relationship. **Conclusion:**Your analysis will provide insights into whether higher speed limits are associated with increased death rates, which can inform policy decisions on road safety.---

Solution: Let x= Speed limit ( Miles per hour) and y = Death rate x y (x-x) (x-x)2 (y-y) (y-y)2 (x-x)(y-y) 54 3.1 -5.5 30.25 -1.24 1.5376 6.82 54 3.4 -5.5 30.25 -0.94 0.8836 5.17 54 3.5 -5.5 30.25 -0.84 0.7056 4.62 69 3.6 9.5 90.25 -0.74 0.5476 -7.03 54 4.2 -5.5 30.25 -0.14 0.0196 0.77 59 4.4 -0.5 0.25 0.06 0.0036 -0.03 54 4.8 -5.5 30.25 0.46 0.2116 -2.53 64 5 4.5 20.25 0.66 0.4356 2.97 59 5.2 -0.5 0.25 0.86 0.7396 -0.43 74 6.2 14.5 210.25 1.86 3.4596 26.97 n = 10 observation ∑x= 595x= ∑xn=59510=59.5∑y= 43.4y=∑yn=43.410=4.34∑(x-x)2=472.5∑(y-y)2=8.544∑(x-x)(y-y)= 37.3a) The scatter diagram of the data is b) To find the sample correlation coefficient r r= ∑(x-x)(y-y)∑(x-x)2×∑(y-y)2r= 37.3472.5×8.544r= 37.34037.04r=37.363.537705=0.587053r= 0.59 The correlation coefficient of the data is 0.59