Question

Use a scatterplot and the linear correlation coefficient r to determine whether there is a correlation between the two variables. Use alphaequals0.05. x 6 1 4 8 5 y 5 0 2 7 4 Click here to view a table of critical values for the correlation coefficient. LOADING... Does the given scatterplot suggest that there is a linear​ correlation? A. Yes comma because the points appear to have a straight line pattern. B. ​Yes, because the data does not follow a straight line. C. ​No, because the data follows a straight line. D. No comma because the points do not appear to have a straight line pattern. 0 4 8 12 0 4 8 12 x y x y graph Does the correlation coefficient indicate that there is a linear correlation between the​ variables? A. ​No, because the absolute value of the correlation coefficient is greater than the critical value. B. No comma because the absolute value of the correlation coefficient is less than the critical value. C. Yes comma because the absolute value of the correlation coefficient is greater than the critical value. D. ​Yes, because the absolute value of the correlation coefficient is less than

Answer 1

Does the given scatterplot suggest that there is a linear​ correlation?

A. Yes, because the points appear to have a straight line pattern.

Explanation:

The scatterplot for the given two variables x and y is given as below:

From above scatter plot, it is observed that there is linear relationship exists between the given two variables as the points appear to have a straight line pattern.

Does the correlation coefficient indicate that there is a linear correlation between the​ variables?

C. Yes, because the absolute value of the correlation coefficient is greater than the critical value.

Solution:

The correlation coefficient between the given two variables is given as 0.986621 (by using excel), this means there is strong positive linear relationship exists between the given two variables.

H₀: ρ = 0 versus H_a: ρ ≠ 0

This is a two tailed test.

We are given

Correlation coefficient = r = 0.986621

Level of significance = α = 0.05

n = 5

df = n – 2 = 5 – 2 = 3

So, critical value by using critical value table is given as below:

Critical value = 0.878

Correlation coefficient r = 0.986621 > Critical value = 0.878

So, we reject the null hypothesis

There is sufficient evidence to conclude that the given correlation coefficient is statistically significant.