9.1

1.

Describe the range of values for the correlation coefficient.

Choose the correct answer below.

A.

The range of values for the correlation coefficient is 1 to1, not inclusive.

B.

The range of values for the correlation coefficient is 0 to1, inclusive.

C.

The range of values for the correlation coefficient is 0 to1, not inclusive

D.

The range of values for the correlation coefficient is 1 to1, inclusive.

2.

Which value of r indicates a strongercorrelation: r=0.831 or r=0.889? Explain your reasoning.

Choose the correct answer below.

A.

r=0.831 represents a stronger correlation because 0.889>0.831.

B.

r=0.889 represents a stronger correlation because 0.889>0.831.

C.

r=0.889 represents a stronger correlation because 0.831>0.889.

D.

r=0.831 represents a stronger correlation because 0.831>0.889.

3.

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.1 Click here to view the table of critical values for the Pearson correlation coefficient.2

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

A.

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, 650); (5, 600); (5, 300); (6, 250); (6, 0). The points follow a general trend of falling from left to right at a constant rate. All vertical 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, 0); (2, 250); (2, 300); (3, 600); (3, 650); (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.

C.

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); (250, 6); (300, 5); (600, 5); (650, 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.

D.

0

1500

3000

0

2

4

6

8

Age(years)

Vocabularysize

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); (250, 2); (300, 2); (600, 3); (650, 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=

(Round to three decimal places asneeded.)

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

There is (1) linear correlation.

Interpret the correlation. Choose the correct answer below.

A.

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

B.

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

C.

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

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.

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

F.

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

(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

. Therefore, there (2) sufficient evidence at the 1% level of significance to conclude that (3) betweenchildren's ages and the number of words in their vocabulary.

(Round to three decimal places asneeded.)

1: Data TableAge, x

Vocabularysize, y

1

4

2

230

3

580

4

1200

5

2100

6

2500

3

640

5

2200

2

280

4

1100

6

2400

2: Critical Values for the Pearson Correlation Coefficient

Critical Values for the Pearson Correlation Coefficient. The correlation is significant when the absolute value of r is greater than the value in the table. The values are given in the copyable data table.

(1)a perfect negative

a perfect positive

a weak negative

a strong positive

no

a strong negative

a weak positive

(2)is not

is

(3)there is no correlation

there is a significant linear correlation

4.

The accompanying table shows eleven altitudes(in thousands offeet) and the speeds of sound(in feet persecond) at these altitudes. Complete parts(a) through(d) below.

Click here to view the data table.3 Click here to view the table of critical values for the Pearson correlation coefficient.4

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

A.

940

1140

-5

55

Altitude(1000'sft)

Speedofsound(ft/s)

A scatter plot has a horizontal axis labeled Altitude (thousands of feet) from 940 to 1140 in increments of 20 and a vertical axis labeled Speed of sound (feet per second) from negative 5 to 55 in increments of 5. The following 11 points are plotted: (967, 0); (967, 5); (967, 10); (968, 15); (994, 20); (1016, 25); (1035, 30); (1058, 35); (1077, 40); (1098, 45); (1116, 50). From left to right, the first 3 points follow the pattern of a vertical line and the next 8 points tightly follow the pattern of a line that rises from left to right. All horizontal coordinates are approximate.

B.

940

1140

-5

55

Altitude(1000'sft)

Speedofsound(ft/s)

• scatter plot has a horizontal axis labeled Altitude (thousands of feet) from 940 to 1140 in increments of 20 and a vertical axis labeled Speed of sound (feet per second)from negative 5 to 55 in increments of 5. The following 11 points are plotted: (967, 50); (967, 45); (967, 40); (968, 35); (994, 30); (1016, 25); (1035, 20); (1058, 15); (1077, 10); (1098, 5); (1116, 0). From left to right, the first 3 points follow the pattern of a vertical line and the next 8 points tightly follow the pattern of a line that falls from left to right. All horizontal coordinates are approximate.

C.

-5

55

940

1140

Altitude(1000'sft)

Speedofsound(ft/s)

A scatter plot has a horizontal axis labeled Altitude (thousands of feet) from negative 5 to 55 in increments of 5 and a vertical axis labeled Speed of sound (feet per second) from 940 to 1140 in increments of 20. The following 11 points are plotted: (0, 1116); (5, 1098); (10, 1077); (15, 1058); (20, 1035); (25, 1016); (30, 994); (35, 968); (40, 967); (45, 967); (50, 967). From left to right, the first 8 points tightly follow the pattern of a line that falls from left to right, and the next 3 points follow the pattern of a horizontal line. All vertical coordinates are approximate.

D.

-5

55

940

1140

Altitude(1000'sft)

Speedofsound(ft/s)

A scatter plot has a horizontal axis labeled Altitude (thousands of feet) from negative 5 to 55 in increments of 5 and a vertical axis labeled Speed of sound (feet per second) from 940 to 1140 in increments of 20. The following 11 points are plotted: (0, 967); (5, 967); (10, 967); (15, 968); (20, 994); (25, 1016); (30, 1035); (35, 1058); (40, 1077); (45, 1098); (50, 1116). From left to right, the first 3 points follow the pattern of a horizontal line and the next 8 points tightly follow the pattern of a line that rises from left to right. All vertical coordinates are approximate.

(b) Calculate the sample correlation coefficient r.

r=

(Round to three decimal places asneeded.)

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

There is (1) linear correlation.

Interpret the correlation. Choose the correct answer below.

A.

Based on thecorrelation, there does not appear to be a linear relationship between altitude and speed of sound.

B.

As altitudeincreases, speeds of sound tend to decrease.

C.

As altitudeincreases, speeds of sound tend to increase.

D.

Higher altitudes cause increases in speeds of sound.

E.

Based on thecorrelation, there does not appear to be any relationship between altitude and speed of sound.

F.

Higher altitudes cause decreases in speeds of sound.

(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 (2) sufficient evidence at the 1% level of significance to conclude that (3) between altitude and speed of sound.

(Round to three decimal places asneeded.)

3: Data TableAltitude, x

Speed ofsound, y

0

1115.7

5

1097.5

10

1077.1

15

1057.7

20

1035.2

25

1015.7

30

994.4

35

968.1

40

966.8

45

966.8

50

966.8

4: Critical Values for the Pearson Correlation Coefficient

Critical Values for the Pearson Correlation Coefficient. The correlation is significant when the absolute value of r is greater than the value in the table. The values are given in the copyable data table.

(1)a weak positive

no

a perfect negative

a strong positive

a weak negative

a perfect positive

a strong negative

(2)is

is not

(3)there is a significant linear correlation

there is no correlation