Question

use the given data set to complete parts (a) through (c) below. (use α = 0.05.)

x	y
8	6.77
13	12.74
9	7.11
11	7.81
14	8.83
6	6.08
4	5.38
12	8.15
7	6.43
5	5.72

click here to view a table of critical values for the correlation coefficient.
a. construct a scatterplot. choose the correct graph below.
a. graph a
b. graph b
c. graph c
d. graph d

Explanation:

Step1: Analyze the scatter - plot coordinates

We know that in a scatter - plot, the \(x\) - values and \(y\) - values are plotted as ordered pairs \((x,y)\). For example, when \(x = 4\), we look for the corresponding \(y\) - value in the data set.

Step2: Check each option

• Option A:
• The \(x\) - axis and \(y\) - axis are mis - labeled. In a standard scatter - plot for this data set (where we assume \(x\) is the independent variable and \(y\) is the dependent variable), the values on the axes do not match the data points. For example, if we consider the general trend of the data, the \(y\) - values for larger \(x\) - values (like \(x = 13\) with \(y=12.74\)) do not follow the pattern in this graph.
• Option B:
• The \(y\) - axis values decrease as \(x\) - axis values increase, which is contrary to the positive - correlation trend (if we calculate the covariance or just observe the general movement of points). For example, when \(x\) goes from \(4\) (\(y = 5.38\)) to \(5\) (\(y = 5.72\)), \(y\) should increase slightly, but in this graph, it does not follow this for the overall trend.
• Option C:
• There are some out - of - pattern points. For example, if we consider the general increasing trend (as \(x\) increases, \(y\) should generally increase), but in this graph, there are points that deviate in a non - random way that is not supported by the data set.
• Option D:
• When \(x = 4\), \(y = 5.38\); when \(x=5\), \(y = 5.72\); when \(x = 6\), \(y=6.08\); when \(x = 7\), \(y = 6.43\); when \(x = 8\), \(y = 6.77\); when \(x = 9\), \(y = 7.11\); when \(x = 10\), \(y = 7.46\); when \(x = 11\), \(y = 7.81\); when \(x = 12\), \(y = 8.15\); when \(x = 13\), \(y = 12.74\); when \(x = 14\), \(y = 8.83\). The points in this scatter - plot follow the general trend of the data set, with \(y\) increasing as \(x\) increases (with some minor fluctuations that can be due to data variability)

Answer:

D.