Question

use the given data set to complete parts (a) through (c) below (use a = 0.05.)
x\ty
10\t7.46
8\t6.76
13\t12.74
9\t7.11
11\t7.82
14\t8.84
6\t6.08
4\t5.38
12\t8.16
7\t6.43
5\t5.73
click here to view a table of critical values for the correlation coefficient.

1. construct a scatterplot. choose the correct graph below

oa.
graph a
ob.
graph b
oc.
graph c
od.
graph d

Explanation:

Step1: List Data Points

Extract (x, y) pairs from the table: (10,7.46), (8,6.76), (13,12.74), (9,7.11), (11,7.82), (14,8.84), (6,6.08), (4,5.38), (12,8.16), (7,6.43), (5,5.73).

Step2: Analyze x and y Ranges

x ranges from 4 to 14, y from ~5.38 to 12.74. Check scatterplot axes (x: 0 - 16, y: 0 - 16).

Step3: Match Points to Graphs

• Graph A: Check if points align. For x=13, y=12.74 (should be near (13,13)), x=14, y=8.84 (near (14,9)), x=4, y=5.38 (near (4,5)). Wait, re - evaluate. Wait, let's check the correct scatterplot. Wait, the data has x and y where as x increases, y generally increases? Wait no, wait the data: x=4 (y=5.38), x=5 (5.73), x=6 (6.08), x=7 (6.43), x=8 (6.76), x=9 (7.11), x=10 (7.46), x=11 (7.82), x=12 (8.16), x=13 (12.74), x=14 (8.84). Wait, x=13 has a high y (12.74), x=14 has y=8.84. Wait, maybe I misread. Wait the table: x=13, y=12.74; x=14, y=8.84. Now, looking at the graphs:

Graph B: Has a point at x=13, y=12 (approx) and x=14, y=9 (approx). Let's check the other points. For x=4, y=5.38 (near (4,5)), x=5, y=5.73 (near (5,6)), x=6, y=6.08 (near (6,6)), x=7, y=6.43 (near (7,6)), x=8, y=6.76 (near (8,7)), x=9, y=7.11 (near (9,7)), x=10, y=7.46 (near (10,7)), x=11, y=7.82 (near (11,8)), x=12, y=8.16 (near (12,8)), x=13, y=12.74 (near (13,13)), x=14, y=8.84 (near (14,9)). Now check graph B: the main cluster is from x=4 - 12, y=5 - 8, with two points at x=13 (y~13) and x=14 (y~9). Wait, no, maybe I made a mistake. Wait the correct scatterplot should plot each (x,y) correctly. Let's re - check the data:

Wait the data points:

(4,5.38), (5,5.73), (6,6.08), (7,6.43), (8,6.76), (9,7.11), (10,7.46), (11,7.82), (12,8.16), (13,12.74), (14,8.84)

Now, when we plot these, the first nine points (x=4 to 12) have y increasing with x (linear trend), then x=13 has a jump to y=12.74, and x=14 has y=8.84 (which is higher than x=12's y=8.16 but lower than x=13's y=12.74). Now, looking at the graphs:

Graph B: Let's see the points. The cluster from x=4 - 12, y=5 - 8, then x=13 (y~13) and x=14 (y~9). Wait, maybe the correct graph is B? Wait no, wait the original problem's graph B: looking at the image, graph B has a cluster of points from x=6 - 12, y=5 - 8, and two points at x=13, y=12 and x=14, y=9. Wait, maybe I messed up. Wait, let's check the x and y values again. Wait x=13, y=12.74: so (13,12.74) is close to (13,13). x=14, y=8.84 is close to (14,9). x=4, y=5.38 is (4,5.38) ~ (4,5). Now, graph B: does it have a point at (4,5)? Let's see the graphs:

Graph A: The left - most point is at x=4, y=5 (approx). Graph B: left - most point? Wait, the data has x=4 (y=5.38), x=5 (5.73), x=6 (6.08), etc. Let's check the correct scatterplot. Wait, maybe the correct graph is the one where the points are plotted as per the (x,y) pairs. After re - evaluating, the correct scatterplot is the one that matches the (x,y) coordinates. Based on the data, the correct graph is the one labeled B? Wait, no, wait the user's image: let's re - check. Wait, the data points: when x=13, y=12.74 (so a point at (13,12.74)), x=14, y=8.84 (14,8.84). Looking at graph B, there is a point at x=13, y=12 (approx) and x=14, y=9 (approx), and the other points form a line from x=4 to x=12, y increasing. So the correct graph is B.

Answer:

B (the graph labeled B)