Question

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 α = 0.01. 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 | 7.0 | 7.5 | 9.8 | 9.4 | 8.6 | 8.4
weight | 109 | 194 | 250 | 204 | 193 | 192

click here to view a table of critical values for the correlation coefficient.

the linear correlation coefficient is r = 0.845
(round to three decimal places as needed.)

the critical values are r = 0.917
(round to three decimal places as needed. use a comma to separate answers as needed.)

because the absolute value of the linear correlation coefficient is than the positive critical value, there sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals for a significance level of α = 0.01.

Explanation:

Step1: Compare |r| and critical value

The linear correlation coefficient \( r = 0.845 \), so \( |r| = 0.845 \). The critical value is \( 0.917 \). Since \( 0.845 < 0.917 \), the absolute value of \( r \) is less than the positive critical value.

Step2: Determine evidence

In correlation testing, if \( |r| \) is less than the critical value, we fail to reject the null hypothesis (no linear correlation). So there is not sufficient evidence.

Answer:

Because the absolute value of the linear correlation coefficient is less than the positive critical value, there is not sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals for a significance level of \( \alpha = 0.01 \).

(First blank: less; Second blank: is not)