Question

Use the given data set to complete parts (a) through (C) below. (Use a = 0.05.) 10 9.14 8 8.15 13 8.74 9 8.77 11 9.27 14 8.09 6 6.13 4 3.09 12 9.13 5 4.75 7.26 Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot. Choose the correct graph below. OA OB. OC. OD. AY 10- 8 10- 10 8 10- 8- 6 6- 6- . 6- 4 4 4- 4 4 2 ........... 2- 8 12 16 12 16 12 16 12 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 r= (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. O A. There is insufficient evidence to support the claim of a linear correlation between the two variables. O B. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables. OC. There is sufficient evidence to support the claim of a linear correlation between the two variables OD. There is sufficient 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. O A. The scatterplot does not reveal a distinct pattern. OB. The scatterplot reveals a distinct pattern that is not a straight-line pattern. O C. The scatterplot reveals a distinct pattern that is a straight-line pattern with positive slope. OD. The scatterplot reveals a distinct pattern that is a straight-line pattern with negative slope. Click to select your answer(s). ?

Answer 1

The scatter plot of the data is :

10 9 0 100 7 6 5. 4 3 2 1 0 0 2 4 6 8 10 12 14 16

Option (C) is correct.

b) r = 0.815

$t=\frac{r\sqrt{n-2}}{\sqrt{1-r^{2}}}=4.22$

$t_{\frac{0.05}{2};9}=2.262$

since t > t _crit so we could say there is sufficient evidence to support the claim of linear correlation between the 2 variables (C)

c) The scatter plot reveals a distinct pattern that is not a straight line pattern.