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 7 5 y 9.14 8.14 8.75 8.77 9.26 8.11 6.13 3.09 9.12 7.26 4.74 LOADING... Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot. Choose the correct graph below. A. 0 4 8 12 16 0 2 4 6 8 10 x y 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. 0 4 8 12 16 0 2 4 6 8 10 x y 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, 2); (5, 2.6); (6, 3); (7, 3.6); (8, 4); (9, 4.6); (10, 5); (11, 5.6); (12, 6); (13, 6.6); (14, 7). C. 0 4 8 12 16 0 2 4 6 8 10 x y 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, 3); (5, 4.8); (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). D. 0 4 8 12 16 0 2 4 6 8 10 x y 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. 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 insufficient evidence to support the claim of a nonlinear correlation between the two variables. B. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. C. There is insufficient evidence to support the claim of a linear correlation between the two variables. D. There is sufficient 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 distinct pattern that is a? straight-line pattern with negative slope. B. The scatterplot reveals a distinct pattern that is a? straight-line pattern with positive slope. C. The scatterplot does not reveal a distinct pattern. D. The scatterplot reveals a distinct pattern that is not a? straight-line pattern. Click to select your answer(s).

Answer 1

Solution : -

scatter plot

1). The option 'C' is correct.

(C.) 0 4 8 12 16 0 2 4 6 8 10 x y 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, 3); (5, 4.8); (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).

2) . Correlation Coefficient :

using this formula , the correlation coefficient between x and y is,

Hypothesis :

Vs  

Ho: There is no correlation between the two variables.

H₁ : There is nonlinear correlation between the two variables.

test statistics ,

p-value = 0.002143 < alpha = 0.05

hence , We reject Ho and conclude that

i.e. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. [ option B. is correct ]

3). From the Scatter plot , We can See that

The scatterplot reveals a distinct pattern that is not a? straight-line pattern.

[ option D is correct ]