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

alphaαequals=0.010.01.

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	7.17.1	7.77.7	9.69.6	9.49.4	8.88.8	8.18.1
Weight	112112	197197	241241	205205	202202	179179

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

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Construct a scatterplot. Choose the correct graph below.

A.

710100300width (cm)weight (kg)

A scatterplot has a horizontal scale labeled “width in centimeters” from 7 to 10 in increments of 0.5 and a vertical scale labeled “weight in kilograms” from 100 to 300 in increments of 20. Six points are plotted with approximate coordinates as follows: (7.4, 160); (7.6, 195); (8.2, 200); (8.9, 220); (9.3, 205); (9.9, 290).

B.

710100300width (cm)weight (kg)

A scatterplot has a horizontal scale labeled “width in centimeters” from 7 to 10 in increments of 0.5 and a vertical scale labeled “weight in kilograms” from 100 to 300 in increments of 20. Six points are plotted with approximate coordinates as follows: (7.1, 290); (7.7, 205); (8.1, 220); (8.8, 200); (9.4, 195); (9.6, 160).

C.

710100300width (cm)weight (kg)

A scatterplot has a horizontal scale labeled “width in centimeters” from 7 to 10 in increments of 0.5 and a vertical scale labeled “weight in kilograms” from 100 to 300 in increments of 20. Six points are plotted with approximate coordinates as follows: (7.1, 110); (7.7, 195); (8.1, 180); (8.8, 200); (9.4, 205); (9.6, 240).

D.

710100300width (cm)weight (kg)

A scatterplot has a horizontal scale labeled “width in centimeters” from 7 to 10 in increments of 0.5 and a vertical scale labeled “weight in kilograms” from 100 to 300 in increments of 20. Six points are plotted with approximate coordinates as follows: (7.4, 240); (7.6, 205); (8.2, 200); (8.9, 180); (9.3, 195); (9.9, 110).The linear correlation coefficient r is

nothing.

​(Round to three decimal places as​ needed.)

The critical values are

requals=nothing.

​(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

▼

less

greater

than the positive critical​ value, there

▼

is

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

alphaαequals=0.010.01.

Click to select your answer(s).

Answer 1

1. The correct option is C, i.e.

A scatterplot has a horizontal scale labeled “width in centimeters” from 7 to 10 in increments of 0.5 and a vertical scale labeled “weight in kilograms” from 100 to 300 in increments of 20. Six points are plotted with approximate coordinates as follows: (7.1, 110); (7.7, 195); (8.1, 180); (8.8, 200); (9.4, 205); (9.6, 240).

2. The linear correlation coefficient r is 0.855

(The calculations and Scatter plot are provided below)

3. degree of freedom, d = no. of observations - 2 = 6-2 = 4

So, critical value at (d=4) and (α=0.01) = 4.602 ( Obtained from a t-distribution table)

4. Because the absolute value of the linear correlation coefficient is less than the positive critical​ value, there

is 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=0.010.01.

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