Question

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use

alphaαequals=​0.05.)

x	1010	88	1313	99	1111	1414	66	44	1212	77	55
y	7.467.46	6.766.76	12.7412.74	7.117.11	7.827.82	8.848.84	6.086.08	5.385.38	8.168.16	6.436.43	5.735.73

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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, 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).

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 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).

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, 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).

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 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).

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 nonlinear 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 linear 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.

Answer 1

1. D 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).

2. r=0.818.

The test statistic for t test of curtain test is 4.258. Which is significant. Thus conclusion is

C.There is sufficient evidence to support the claim of a linear correlation between the two variables.

3. C.
The scatterplot reveals a perfect​ straight-line pattern, except for the presence of one outlier.