Use the given data set to complete parts (a) through (c) below. (Use alphaequals
ID: 3360414 • Letter: U
Question
Use the given data set to complete parts (a) through (c) below. (Use
alphaequals=0.05.)
x
10
8
13
9
11
14
6
4
12
77
55
y
7.45
6.77
12.74
7.11
7.81
8.84
6.09
5.38
8.14
6.42
5.735.73
LOADING...
Click here to view a table of critical values for the correlation coefficient.
a. Construct a scatterplot. Choose the correct graph below.
A.
04812160481216xy
A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 1); (5, 1.4); (6, 1.6); (7, 2); (8, 2.4); (9, 3); (10, 3.6); (11, 4.2); (12, 4.8); (13, 6); (14, 8).
B.
04812160481216xy
A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 16 in increments of 2. Eleven points are plotted with approximate coordinates as follows: (4, 5.4); (5, 5.8); (6, 6); (7, 6.4); (8, 6.8); (9, 7.2); (10, 7.4); (11, 7.8); (12, 8.2); (13, 12.8); (14, 8.8).
C.
04812160481216xy
A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 6); (5, 5.6); (6, 5); (7, 4.6); (8, 4); (9, 3.6); (10, 3); (11, 2.6); (12, 2); (13, 1.6); (14, 1).
D.
04812160481216xy
A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Ten points are plotted with approximate coordinates as follows: (4, 3.2); (6, 6.2); (7, 7.2); (8, 8.2); (9, 8.8); (10, 9.2); (11, 9.2); (12, 9.2); (13, 8.8); (14, 8.2).
b. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.
The linear correlation coefficient is
requals=nothing.
(Round to three decimal places as needed.)
Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below.
A.
There is
sufficientsufficient
evidence to support the claim of a nonlinear correlation between the two variables.
B.
There is
insufficientinsufficient
evidence to support the claim of a linear correlation between the two variables.
C.
There is
sufficientsufficient
evidence to support the claim of a linear correlation between the two variables.
D.
There is
insufficientinsufficient
evidence to support the claim of a nonlinear correlation between the two variables.
c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot. Choose the correct answer below.
A.
The scatterplot reveals a perfect straight-line pattern and does not contain any outliers.
B.
The scatterplot does not reveal a perfect straight-line pattern.
C.
The scatterplot reveals a perfect straight-line pattern, except for the presence of one outlier.
D.
The scatterplot does not reveal a perfect straight-line pattern, and contains one outlier.
Explanation / Answer
The statistical software output for this problem is:
Correlation between x and y is:
0.81597031
Hence,
a) Option B is correct.
b) r = 0.816
Option C is correct.
c) The scatterplot reveals a perfect straight-line pattern, except for the presence of one outlier.
Option C is correct.
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