Question

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

x,y

10,9.14

8,8.15

13,8.75

9,8.77

11,9.25

14,8.09

6,6.13

4,3.09

12,9.14

7,7.25

5,4.73

A - Construct a scatterplot.

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 = ______?

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

B- There is insufficient evidence to support the claim of a linear correlation between the two variables.

C- There is insufficient evidence to support the claim of a nonlinear correlation between the two variables.

D- 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.

A- The scatterplot reveals a distinct pattern that is a​straight-line pattern with positive slope.

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

C- The scatterplot reveals a distinct pattern that is a​straight-line pattern with negative slope.

D- The scatterplot does not reveal a distinct pattern.

Answer 1

A- There is sufficient evidence to support the claim of a linear correlation between the two variables

Explanation:

x y

10 9.14

8 8.15

13 8.75

9 8.77

11 9.25

14 8.09

6 6.13

4 3.09

12 9.14

7 7.25

5 4.73

r 0.81602411

Thus correlation coefficient is 0.816 a strong positive correlation.

`H_0: r=0\\H_a: r \\eq 0`

(two tailed test)

Test statistic t =
`(r√(n-2) )/(√(1-r^2) ) \\=7.327`

p value <0.05 our significant level

Hence reject H0, there is correlation significant between the two variables.

A- There is sufficient evidence to support the claim of a linear correlation between the two variables

Scatter plot is attached.