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

x y

5 37.22

6 34.23

7 34.84

8 31.25

9 25.96

10 23.37

11 20.58

12 19.69

13 16.2

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

x y

2 5.98

3 15.27

4 15.96

5 18.65

6 24.04

7 25.53

8 28.22

9 32.81

(select one)

A) Yes, significant correlation

B) No

3) Write (an) equation in the formy=mx+b for the following table:

x y

-4 -26

-2 -12

0 2

2 16

4 30

6 44

8 58

10 72

y=

4) 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 the0.05significance level.

a) If we useL to denote the low income group andH to denote the high income group, identify the correct alternative hypothesis. ( select one)

A)H1:0

B) H1:=0

C) H1:pLpH

D) H1:r0

E) H1:0

b) Thercorrelation 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

A) RejectH0

B) Fail to rejectH0

e) Which means

A) The sample data supports the claim

B) There is sufficient evidence to warrant rejection of 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 incomex) 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

5) 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 the0.05significance level.

a) If we useM to denote the midterm exam scores andF to denote the final exam scores, identify the correct alternative hypothesis.

A) H1:0

B) H1:=0

C) H1:r0

D) H1:0

E) H1:pMpF

b) Ther 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) RejectH0

B) Fail to rejectH0

e) Which means

A) The sample data supports the claim

B) There is not sufficient evidence to support the claim

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

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

f) The regression equation (in terms of incomex) 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

6) 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 12.94

7 10.43

8 13.62

9 15.41

10 18.4

11 18.79

12 18.38

13 21.77

14 24.26

15 25.15

7) Suppose that you run a correlation and find the correlation coefficient is 0.379 and the regression equation isy^=2.2x+6.96. Also,x=4.2andy=16.1.

If the critical value is .279, use the appropriate method to predict theyvalue whenxis 1.7

( )

8) 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 (H1:0). You have a data set with 5 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of=0.05.

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

r_c.v.=

Report answer accurate to three decimal places

Use the critical value table above

9) Suppose that you run a correlation and find the correlation coefficient is -0.514 and the regression equation isy^=-3.3x+37.92. The mean values of your data werex=5.4 andy=20.3.

If the critical value is .632, use the appropriate method to predict they value whenx is 6.9

10) Monthly high temperatures in a certain location have been tracked for several months. LetX represent the month andY the high temperature (in degrees Fahrenheit). Based on the data shown below, at the 0.05 significance level, is the correlation significant?

x y

1 16.9

2 7.86

3 16.82

4 6.28

5 5.24

6 0.7

7 5.66

8 18.12

9 -0.92

10 17.04

11 11

(select one)

A) No, not a significant correlation

B) Yes, significant correlation

You intend to predict the high temperature in month 13 using the sample data. Which of the following is the best prediction:

A) between 4.59 and 14.44 degrees

B) -11.49 degrees

C) 8.12 degrees

D) between 3.63 and 8.37 degrees

11) You intend to conduct a goodness-of-fit test for a multinomial distribution with 3 categories. You collect data from 54 subjects.

What are the degrees of freedom for the2 distribution for this test?

d.f. =

12) 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 15

B 15

C 5

D 25

E 5

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.

13) 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 10

B 25

C 25

D 15

E 15

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.

14) You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: Ho : pA=0.2;pB=0.3;pC=0.3;pD=0.2

Complete the table. Do not round your expected frequencies.

Category Observed Frequency Expected Frequency

A 42

B 54

C 47

D 46

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) Fail to reject the Null Hypothesis

B) Reject the Null Hypothesis

Report all answers accurate to three decimal places.

15) You intend to conduct a test of independence for a contingency table with 8 categories in the column variable and 5 categories in the row variable. You collect data from 1270 subjects.

What are the degrees of freedom for the2 distribution for this test?

d.f. =

16) 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

A11 2759

B35 2315

(a) What is the chi-squaretest-statisticfor this data?

Test Statistic: (round to 3 decimal places)

2=

(b) What is thep-valuefor 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 0.025 significance level?

A) There isnotsufficient evidence to warrantrejectionof the claim that the row and column variables are dependent.

B) There isnotsufficient evidence tosupportthe claim that the row and column variables are dependent.

C) Thereissufficient evidence to warrantrejectionof the claim that the row and column variables are dependent.

D) Thereissufficient evidence tosupportthe claim that the row and column variables are dependent.

17) 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

A17 2931

B34 4222

(a) What is the chi-squaretest-statisticfor this data?

Test Statistic: (round to 3 decimal places)

2=

(b) What is thep-valuefor 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 0.01 significance level?

A) There isnotsufficient evidence tosupportthe claim that the row and column variables are dependent.

B) There isnotsufficient evidence to warrantrejectionof the claim that the row and column variables are dependent.

C) Thereissufficient evidence to warrantrejectionof the claim that the row and column variables are dependent.

D) Thereissufficient evidence tosupportthe claim that the row and column variables are dependent.