Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using alphaαequals=0.050.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?

Overhead Width

7.27.2

7.67.6

9.89.8

9.29.2

8.78.7

8.28.2

Weight

119119

174174

245245

197197

196196

187187

Hypotheses:

H o - There is no linear correlation.

H 1 - There is linear correlation.

We will reject H o if the absolute value of r is greater than the critical value in the table. For α = 0.05 and n = 6, the critical value is 0.811.

The linear coefficient r:

r = [ (n * ∑ x y) - ∑x∑y ]/√ (n*∑x² - (∑x) ²) * √ (n*∑y² - (∑y) ²) =

= (6 * 9,631.2 - 50.7 * 1,118) : (√ (6 * 433.21 - 50.7²) * √ (6*216,656 - 1,118²)

r = 1,104 : 1,199.517

r = 0.92

r > 0.811

Answer:

Because the absolute value of the linear correlation coefficient is greater than the positive critical value, there is sufficient evidence to claim that there is linear correlation between overhead width of the seals and the weight of the seals for the significance level of α = 0.05.