A department of transportation's study on driving speed and miles per gallon for midsize automobiles resulted in the following data:

Speed (Miles per Hour)30,50,40,55,30,24,61,25,50,55 Miles per Gallon 28,24,24,22,31,33,20,35,25,24

Compute the sample correlation coefficient (to decimals and enter negative value as negative number).

What can you conclude, based on your computation of the sample correlation coefficient?

• Select your answer -There is a strong positive linear relationship. There is a moderate positive linear relationship. There is neither a positive nor a negative linear relationship. There is a strong negative linear relationship. There is a moderate negative linear relationship.

Item 2 Select the correct interpretation for the sample correlation coefficient. (i) For driving speeds between and miles per hour, higher speeds are associated with higher miles per gallon. (ii) For driving speeds between and miles per hour, higher speeds are associated with lower miles per gallon. (iii) For driving speeds between and miles per hour, lower speeds are associated with lower miles per gallon. (iv) There is no relationship between driving speed and miles per gallon.

Let me solve this step by step.

First, let's organize our data: Speed (x): 30, 50, 40, 55, 30, 24, 61, 25, 50, 55 MPG (y): 28, 24, 24, 22, 31, 33, 20, 35, 25, 24 To find correlation coefficient (r), we'll use the formula: r = Σ((x-x̄)(y-ȳ)) / √[Σ(x-x̄)²][Σ(y-ȳ)²] Let's calculate: x̄ = (30+50+40+55+30+24+61+25+50+55)/10 = 42 ȳ = (28+24+24+22+31+33+20+35+25+24)/10 = 26.6 Now calculate deviations and products: x-x̄: -12, 8, -2, 13, -12, -18, 19, -17, 8, 13 y-ȳ: 1.4, -2.6, -2.6, -4.6, 4.4, 6.4, -6.6, 8.4, -1.6, -2.6 Multiply deviations: Σ((x-x̄)(y-ȳ)) = -16.8 - 20.8 + 5.2 - 59.8 - 52.8 - 115.2 - 125.4 - 142.8 - 12.8 - 33.8 = -574.8 Square deviations: Σ(x-x̄)² = 144 + 64 + 4 + 169 + 144 + 324 + 361 + 289 + 64 + 1 Claude can make mistakes. Please double-check responses.

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