The accompanying table shows the ages(in years) of 11 children and the numbers of words in their vocabulary. Complete parts(a) through(d) below.

Click here to view the data table.LOADING...

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

(a) Display the data in a scatter plot. Choose the correct graph below.

A.

0

1500

3000

0

2

4

6

8

Age(years)

Vocabularysize

A scatter plot has a horizontal axis labeled Age in years from 0 to 3000 in increments of 300 and a vertical axis labeled Vocabulary size from 0 to 8 in increments of 1. The following 11 points are plotted: (0, 6); (200, 6); (250, 5); (550, 5); (700, 4); (1100, 4); (1200, 3); (2100, 3); (2200, 2); (2400, 2); (2500, 1). The points follow a general trend of falling from left to right at a constant rate. All horizontal coordinates are approximate.

B.

0

2

4

6

8

0

600

1200

1800

2400

3000

Age(years)

Vocabularysize

A scatter plot has a horizontal axis labeled Age in years from 0 to 8 in increments of 1 and a vertical axis labeled Vocabulary size from 0 to 3000 in increments of 300. The following 11 points are plotted: (1, 2500); (2, 2400); (2, 2200); (3, 2100); (3, 1200); (4, 1100); (4, 700); (5, 550); (5, 250); (6, 200); (6, 0). The points follow a general trend of falling from left to right at a constant rate. All vertical coordinates are approximate.

C.

0

2

4

6

8

0

600

1200

1800

2400

3000

Age(years)

Vocabularysize

A scatter plot has a horizontal axis labeled Age in years from 0 to 8 in increments of 1 and a vertical axis labeled Vocabulary size from 0 to 3000 in increments of 300. The following 11 points are plotted: (1, 0); (2, 200); (2, 250); (3, 550); (3, 700); (4, 1100); (4, 1200); (5, 2100); (5, 2200); (6, 2400); (6, 2500). From left to right, the points follow a general trend of rising from left to right at a constant rate. All vertical coordinates are approximate.

D.

0

1500

3000

0

2

4

6

8

Age(years)

Vocabularysize

A scatter plot has a horizontal axis labeled Age in years from 0 to 3000 in increments of 300 and a vertical axis labeled Vocabulary size from 0 to 8 in increments of 1. The following 11 points are plotted: (0, 1); (200, 2); (250, 2); (550, 3); (700, 3); (1100, 4); (1200, 4); (2100, 5); (2200, 5); (2400, 6); (2500, 6). The points follow a general trend of rising from left to right at a constant rate. All horizontal coordinates are approximate.

(b) Calculate the sample correlation coefficient r.

r=

nothing

(Round to three decimal places asneeded.)

(c) Describe the type ofcorrelation, ifany, and interpret the correlation in the context of the data.

There is

a perfect positive

a strong positive

a weak positive

a weak negative

a strong negative

a perfect negative

no

linear correlation.

Interpret the correlation. Choose the correct answer below.

A.

Aging causes the number of words inchildren's vocabulary to increase.

B.

As ageincreases, the number of words inchildren's vocabulary tends to decrease.

C.

As ageincreases, the number of words inchildren's vocabulary tends to increase.

D.

Based on thecorrelation, there does not appear to be a linear relationship betweenchildren's ages and the number of words in their vocabulary

E.

Based on thecorrelation, there does not appear to be any relationship betweenchildren's ages and the number of words in their vocabulary.

F.

Aging causes the number of words inchildren's vocabulary to decrease.

(d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let =0.01.

The critical value is

nothing

. Therefore, there

is not

is

sufficient evidence at the 1% level of significance to conclude that

there is a significant linear correlation

there is no correlation

betweenchildren's ages and the number of words in their vocabulary.

(Round to three decimal places asneeded.)

Click to select your answer(s).

Data Table:

Age, x Vocabulary size, y

1 9

2 220

3 540

4 1200

5 2200

6 2500

3 680

5 2100

2 260

4 1100

6 2400