1) Based on the data shown below, calculate the correlation coefficient (to three decimal places).

x y

3 55.11

4 51.04

5 47.57

6 45.9

7 42.13

8 41.66

9 35.79

10 36.12

11 29.35

12 29.48

13 26.31

14 24.24

15 19.57

16 16.8

2) Here is a bivariate data set.

x y

34 15.7

24.8 52.5

15.2 58.6

28.9 25.4

38.7 5.9

35.6 18.9

35.9 9.5

28.7 34

31.5 51.5

43.2 -3.2

-7.21 58.1

23.7 35.2

21.1 28.5

17.4 81.1

25.2 12.5

9.2 85.4

40.7 43.3

12.6 89.9

29.3 23.1

Find the correlation coefficient and report it accurate to three decimal places.

r =

3) At the 0.05 significance level, does the data below show significant correlation?

x y

2 16.02

3 22.48

4 23.84

5 19.3

6 22.16

7 32.72

8 35.58

9 32.34

10 34.7

11 36.96

12 46.72

13 38.68

14 46.84

(select one)

A) Yes, significant correlation

B) No

4) You wish to conduct a hypothesis test to determine if a bivariate data set has a significant correlation among the two variables. That is, you wish to test the claim that there is a correlation (H1:0H1:0 ). You have a data set with 20 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of =0.05=0.05 .

Find the critical value for this test using the table below.

r_c.v. =

Report answer accurate to three decimal places.

Degrees of Freedom: n-2 Critical Value: (+ or -) 0.05 Significance Level

1 0.997

2 0.95

3 0.878

4 0.811

5 0.754

6 0.707

7 0.666

8 0.632

9 0.602

10 0.576

11 0.553

12 0.532

13 0.514

14 0.497

15 0.482

16 0.468

17 0.456

18 0.444

19 0.433

20 0.423

21 0.413

22 0.404

23 0.396

24 0.388

25 0.381

26 0.374

27 0.367

28 0.361

29 0.355

30 0.349

5) You wish to conduct a hypothesis test to determine if a bivariate data set has a significant correlation among the two variables. That is, you wish to test the claim that there is a correlation (H1:0H1:0 ). You have a data set with 19 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of =0.05=0.05 .

Find the critical value for this test using the table below.

r_c.v. =

Report answer accurate to three decimal places.

Degrees of Freedom: n-2 Critical Value: (+ or -) 0.05 Significance Level

1 0.997

2 0.95

3 0.878

4 0.811

5 0.754

6 0.707

7 0.666

8 0.632

9 0.602

10 0.576

11 0.553

12 0.532

13 0.514

14 0.497

15 0.482

16 0.468

17 0.456

18 0.444

19 0.433

20 0.423

21 0.413

22 0.404

23 0.396

24 0.388

25 0.381

26 0.374

27 0.367

28 0.361

29 0.355

30 0.349

6) A sample of 20 children was asked to draw a nickel. The diameter of each nickel was recorded as well as each child's family income. Incomes (in thousands of $) and nickel diameters are shown for each of the 20 samples below:

Income (thousands of $) Coin size (mm)

11 30

26 18

19 18

20 25

26 23

39 23

24 28

30 13

15 25

22 19

79 26

56 23

93 15

93 16

67 27

80 21

52 23

54 19

82 19

73 18

Test the claim that there is significant correlation at the 0.05 significance level.

a) If we use LL to denote the low income group and HH to denote the high income group, identify the correct alternative hypothesis. (select one)

A) H1:=0

B) H1:0

C) H1:r0

D) H1:0

E) H1:pLpH

b) The r correlation coefficient is: (round to 3 decimal places)

c) The critical value is: (round to 3 decimal places)

Use the critical value table below

d) Based on this, we (select one)

A) Reject H0

B) Fail to reject H0

e) Which means (select one)

A) There is sufficient evidence to warrant rejection of the claim

B) The sample data supports the claim

C) There is not sufficient evidence to warrant rejection of the claim

D) There is not sufficient evidence to support the claim

f) The regression equation (in terms of income xx ) is:

y= (round to 2 decimal places)

g) To predict what diameter a child would draw a nickel given family income, it would be most appropriate to:

A) Use the regression equation

B) Use the mean coin size

C) Use the P-Value

D) Use the residual

Degrees of Freedom: n-2 Critical Value: (+ or -) 0.05 Significance Level

1 0.997

2 0.95

3 0.878

4 0.811

5 0.754

6 0.707

7 0.666

8 0.632

9 0.602

10 0.576

11 0.553

12 0.532

13 0.514

14 0.497

15 0.482

16 0.468

17 0.456

18 0.444

19 0.433

20 0.423

21 0.413

22 0.404

23 0.396

24 0.388

25 0.381

26 0.374

27 0.367

28 0.361

29 0.355

30 0.349

7) The midterm and final exam scores for a sample of 18 students were recorded. The scores for the 18 students are shown below:

Midterm Exam Score Final Exam Score

55 72

69 80

68 63

53 78

53 62

50 76

63 73

60 69

54 64

82 80

85 86

86 82

76 99

90 93

81 93

82 91

93 89

95 100

Test the claim that there is significant correlation between midterm and final exam scores at the 0.05 significance level.

a) If we use MM to denote the midterm exam scores and FF to denote the final exam scores, identify the correct alternative hypothesis.

A) H1:0

B) H1:0

C) H1:=0

D) H1:r0

E) H1:pMpF

b) The r correlation coefficient is: (round to 3 decimal places)

c) The critical value is: (round to 3 decimal places)

Use the critical value table above

d) Based on this, we

A) Reject H0H0

B) Fail to reject H0H0

e) Which means

A) There is sufficient evidence to warrant rejection of the claim

B) There is not sufficient evidence to warrant rejection of the claim

C) There is not sufficient evidence to support the claim

D) The sample data supports the claim

f) The regression equation (in terms of income xx ) is:

y^= (round to 2 decimal places)

g) To predict what score a student will make on the final exam, it would be most appropriate to:

A) Use the regression equation

B) Use the mean final exam score

C) Use the p-Value

D) Use the residual

8) Write(an) equation in the form y=mx+b for the following table:

x y

-8 -12

-6 -6

-4 0

-2 6

0 12

2 18

4 24

6 30

y=( )

9) Based on the data shown below, calculate the regression line (round each value to two decimal places)

y =( x + )

x y

5 8.05

6 7.9

7 10.25

8 8.5

9 10.55

10 9.8

11 10.15

12 12.4

13 14.95

14 13.3

15 13.55

16 16

10) Suppose that you run a correlation and find the correlation coefficient is 0.761 and the regression equation is y=4.8 x3.86. Also, x=4.7 and y=18.3 .

If the critical value is .396, use the appropriate method to predict the y value when x is 2.4

( )

11) Suppose that you run a correlation and find the correlation coefficient is 0.468 and the regression equation is y=6.4x7.34. The mean values of your data were x=5.1 and y=24.9.

If the critical value is .632, use the appropriate method to predict the y value when x is 6.9

( )

12) Run a regression analysis on the following bivariate set of data with y as the response variable.

x y

24. 112.8

4.4 -16.4

8.3 -35.7

32.7 19

58.7 136.5

36.9 60.2

-3.2 -41.2

-13.7 -98.6

22.7 -6.1

14.1 6.8

38.6 44.2

16.9 -16.3

28.1 18.7

Predict what value (on average) for the response variable will be obtained from a value of 19.7 as the explanatory variable. Use a significance level of =0.05 to assess the strength of the linear correlation.

What is the predicted response value?

y =

13) You intend to conduct a goodness-of-fit test for a multinomial distribution with 7 categories. You collect data from 95 subjects.

What are the degrees of freedom for the 2 distribution for this test?

d.f. = ( )

14) You are conducting a multinomial Goodness of Fit Hypothesis Test (= 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.

Category Observed Frequency Expected Frequency

A 25

B 20

C 25

D 10

E 25

Report all answers to the indicated number of decimal places.

What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.)

2=

What are the degrees of freedom for this test?

d.f.=

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

The p-value is...

A) less than (or equal to)

B) greater than

This test statistic leads to a decision to...

A) reject the null

B) accept the null

C) fail to reject the null

D) accept the alternative

As such, the final conclusion is that...

A) There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.

B) There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.

C) The sample data support the claim that all 5 categories are equally likely to be selected.

D) There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.

15) You are conducting a multinomial Goodness of Fit Hypothesis Test (= 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.

Category Observed Frequency Expected Frequency

A 20

B 20

C 5

D 20

E 25

Report all answers to the indicated number of decimal places.

What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.)

2=

What are the degrees of freedom for this test?

d.f.=

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

The p-value is...

A) less than (or equal to)

B) greater than

This test statistic leads to a decision to...

A) reject the null

B) accept the null

C) fail to reject the null

D) accept the alternative

As such, the final conclusion is that...

A) There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.

B) There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.

C) The sample data support the claim that all 5 categories are equally likely to be selected.

D) There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.

16) You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:

Ho : pA=0.3;pB=0.2;pC=0.3;pD=0.2

Complete the table. Do not round your expected frequencies.

Category Observed Frequency Expected Frequency

A 39

B 24

C 20

D 40

What is the chi-square test-statistic for this data? (round to 3 decimal places)

2=

What is the P-Value? (round to 4 decimal places)

P-Value =

For significance level alpha 0.01,

What would be the conclusion of this hypothesis test?

A) Reject the Null Hypothesis

B) Fail to reject the Null Hypothesis

Report all answers accurate to three decimal places.

17) You intend to conduct a test of independence for a contingency table with 7 categories in the column variable and 3 categories in the row variable. You collect data from 110 subjects.

What are the degrees of freedom for the 2 distribution for this test?

d.f. =

18) You are conducting a test of the claim that the row variable and the column variable are dependentin the following contingency table.

X Y Z

A 35 25 13

B 33 36 22

(a) What is the chi-square test-statistic for this data?

Test Statistic: (round to 3 decimal places)

2=

(b) What is the p-value for this test of independence?

p-value: (round to 4 decimal places)

p-value =

(c) What is the correct conclusion of this hypothesis test at the 0.005 significance level?

A) There is sufficient evidence to support the claim that the row and column variables are dependent.

B) There is not sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.

C) There is not sufficient evidence to support the claim that the row and column variables are dependent.

D) There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.

19) You are conducting a test of the claim that the row variable and the column variable are dependentin the following contingency table.

X Y Z

A 19 36 17

B 45 51 10

(a) What is the chi-square test-statistic for this data?

Test Statistic: (round to 3 decimal places)

2=

(b) What is the p-value for this test of independence?

p-value: (round to 4 decimal places)

p-value =

(c) What is the correct conclusion of this hypothesis test at the 0.005 significance level?

A) There is sufficient evidence to support the claim that the row and column variables are dependent.

B) There is not sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.

C) There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.

D) There is not sufficient evidence to support the claim that the row and column variables are dependent.