Question

listed below are annual data for various years. the data are the numbers of cars sold (thousands) and the numbers of points scored in the super bowl. construct a scatterplot, find the value of the linear correlation coefficient r, and find the p - value using α = 0.05. is there sufficient evidence to conclude that there is a linear correlation between those two variables? would it be reasonable to expect a correlation?

car sales: 8179, 8218, 8518, 8962, 8636, 8535, 8275, 8142
super bowl points: 62, 70, 43, 74, 43, 57, 56, 53

construct a scatterplot. choose the correct graph below.

a.
graph with car sales on x - axis (8000 - 9000) and super bowl points on y - axis (0 - 100) with data points

b.
graph with car sales on x - axis (8000 - 9000) and super bowl points on y - axis (0 - 100) with data points

c.
graph with car sales on x - axis (8000 - 9000) and super bowl points on y - axis (0 - 100) with data points

d.
graph with car sales on x - axis (8000 - 9000) and super bowl points on y - axis (0 - 100) with data points

Explanation:

Step1: Analyze Car Sales Range

Car sales values: 8179, 8218, 8518, 8962, 8636, 8535, 8275, 8142. These are mostly between 8000 - 9000, with some around 8100 - 8900.

Step2: Analyze Super Bowl Points Range

Super Bowl points: 62, 70, 43, 74, 43, 57, 56, 53. These are between ~40 - 75.

Step3: Match to Scatterplot Axes

We need a scatterplot with x - axis (Car Sales) in 8000 - 9000 range and y - axis (Super Bowl Points) in ~40 - 75 range. Let's check the options:

• Option A: Car Sales x - axis 8000 - 9000, Super Bowl Points y - axis 0 - 100 (matches range). The points' distribution should align with the data. Let's check a few points: (8179, 62), (8218, 70), (8518, 43), (8962, 74). In Option A, the x - axis is 8000 - 9000, y - axis 0 - 100, and the points' positions (e.g., 8179 is near 8000 - 8200, 62 is mid - range y; 8962 is near 9000, 74 is high y) seem to fit. Other options: B has y - axis labeled wrong? Wait, no, the y - axis for Super Bowl Points. Wait, the problem's scatterplot options: let's re - check. The correct scatterplot should have Car Sales (x) from ~8000 - 9000 and Super Bowl Points (y) ~40 - 75. Option A's x - axis is 8000 - 9000, y - axis 0 - 100 (covers 40 - 75). The points in A: when we plot (8142, 53) – 8142 is left on x, 53 on y; (8962, 74) – right on x, high on y. This matches the data's range and the need for x in 8000 - 9000 and y in 40 - 75. Other options may have incorrect axis labeling or range. So the correct graph is Option A.

Answer:

A. (The scatterplot with x - axis "Car Sales" in 8000 - 9000 range and y - axis "Super Bowl Points" in 0 - 100 range, with points distributed according to the data)