QUESTION 1 THE TABLE BELOW CONTAINS INFORMATION ON 48

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Question 1

QUESTION 1 THE TABLE BELOW CONTAINS INFORMATION ON 48

The table below contains information on 48 houses: the value of the house and the amount of rental income in a year that the house brings in ("Capital and rental," 2013). 

Table:  Data of House Value versus Rental

Value

Rental

Value

Rental

Value

Rental

Value

Rental

81000

6656

77000

4576

75000

7280

67500

6864

95000

7904

94000

8736

90000

6240

85000

7072

121000

12064

115000

7904

110000

7072

104000

7904

135000

8320

130000

9776

126000

6240

125000

7904

145000

8320

140000

9568

140000

9152

135000

7488

165000

13312

165000

8528

155000

7488

148000

8320

178000

11856

174000

10400

170000

9568

170000

12688

200000

12272

200000

10608

194000

11232

190000

8320

214000

8528

208000

10400

200000

10400

200000

8320

240000

10192

240000

12064

240000

11648

225000

12480

289000

11648

270000

12896

262000

10192

244500

11232

325000

12480

310000

12480

303000

12272

300000

12480

 

1.  Which of the two scatter plots displayed in the image above the problem script correctly depicts rental income as a function of house value? 

Enter letter corresponding to correct plot

ANSWER: A

 2.  Use technology to determine regression equation between house value and rental income.

Enter regression equation in the format as follows:

y^=a+bx

with slope rounded to nearest thousandth and y-intercept value rounded to nearest integer. Examples of correctly entered answers:

y^=-4210+.348x

y^=67553-1.242x

Linear regression equation calculator:

Correlation and Linear Regression Calculator Applet



ANSWER: y^= 5364 + 0.024x

 3.  Use the regression equation to find the rental income from a house worth $230,000 

Enter amount to nearest dollar; do not include dollar sign, commas, or units of measure

ANSWER: 10884


 4.  Use the regression equation to find the rental income from a house worth $400,000 

Enter amount to nearest dollar; do not include dollar sign or units of measure

ANSWER: 14964


 5.  Which rental income that you calculated do you think is closer to the true rental income?

A.  $10884, since house value producing this annual rental income would fall within range of house value data (rental income value is interpolated)

B.  Both calculations are equally accurate since they are calculated using the same regression equation

C.  $14964, since annual rental income  is extrapolated

Enter letter corresponding to correct answer

ANSWER: A

Question 2

QUESTION 1 THE TABLE BELOW CONTAINS INFORMATION ON 48

The World Bank collected data on the percentage of GDP that a country spends on health expenditures ("Health expenditure," 2013) and also the percentage of women receiving prenatal care ("Pregnant woman receiving," 2013).  The data for the 15 countries where this information are available for the year 2011 is in the table below:

Health Expenditure (% of GDP)

Prenatal Care (%)

9.6

47.9

3.7

54.6

5.2

93.7

5.2

84.7

10.0

100.0

4.7

42.5

4.8

96.4

6.0

77.1

5.4

58.3

4.8

95.4

4.1

78.0

6.0

93.3

9.5

93.3

6.8

93.7

6.1

89.8

1.  Which of the two scatter plots displayed in the image above the problem script correctly depicts percentage of women receiving prenatal care as a function of percentage GDP spent on health expenditure? 

Enter letter corresponding to correct plot

ANSWER: B

 2.  Use technology to determine regression equation between percentage GDP spent on health and percentage of women receiving prenatal care.

Enter regression equation the format as follows:

y^=a+bx

with slope rounded to nearest thousandth and y-intercept value rounded to nearest thousandth. Examples of correctly entered answers:

y^=4.913+17.347x

y^=7.553-11.225x

Linear regression equation calculator:

Correlation and Linear Regression Calculator Applet

ANSWER: y = 69.739 + 1.661x

 3.  Use the regression equation to find the percent of women receiving prenatal care for a country that spends 5.0% of GDP

Enter amount to nearest thousandth; do not include percent sign

ANSWER: 78.044



 4.  Use the regression equation to find the percent of women receiving prenatal care for a country that spends 12.0% of GDP

Enter amount to nearest thousandth; do not include percent sign

ANSWER: 89.671



 5.  Which prenatal care percentage that you calculated do you think is closer to the true percentage?

A.  78.044, since % GDP spent on healthcare producing this percentage of women receiving prenatal care would fall within range of input data (value is interpolated)

B.  Both calculations are equally accurate since they are calculated using the same regression equation

C.  89.670, since data for percentage of women receiving prenatal care is extrapolated

Enter letter corresponding to correct answer

ANSWER: A



Question 3

The table below contains on 48 houses: the value of the house and the amount of rental income in a year that the house brings in ("Capital and rental," 2013). 

Table:  Data of House Value versus Rental

Value

Rental

Value

Rental

Value

Rental

Value

Rental

81000

6656

77000

4576

75000

7280

67500

6864

95000

7904

94000

8736

90000

6240

85000

7072

121000

12064

115000

7904

110000

7072

104000

7904

135000

8320

130000

9776

126000

6240

125000

7904

145000

8320

140000

9568

140000

9152

135000

7488

165000

13312

165000

8528

155000

7488

148000

8320

178000

11856

174000

10400

170000

9568

170000

12688

200000

12272

200000

10608

194000

11232

190000

8320

214000

8528

208000

10400

200000

10400

200000

8320

240000

10192

240000

12064

240000

11648

225000

12480

289000

11648

270000

12896

262000

10192

244500

11232

325000

12480

310000

12480

303000

12272

300000

12480

 

1.  Determine the correlation between variables (if it exists) in this relation.  Which variable is the dependent (output) variable?

A.  Value of house

B.  Annual rental income generated

Enter letter corresponding to correct answer

ANSWER: B

 2.  Using technology, determine coefficient of correlation r

Enter r value to nearest ten-thousandth, with its sign (positive or negative and no spaces).  Examples of correctly entered responses:

+0.7789         -0.4529       +0.9976

Correlation coefficient calculator:

Correlation and Linear Regression Calculator Applet

ANSWER: + 0.7647


 3.  What type of linear correlation does the calculated r value indicate?

A.  Strong positive correlation

B.  Moderate positive correlation

C.  Weak negative correlation

D.  No linear correlation

E.  None of the above are correct

Enter letter corresponding to correct answer

ANSWER: A

 4.  Use the correlation coefficient r to find the coefficient of determination r2

Enter answer rounded to nearest thousandth.  Examples of correctly entered responses:

0.956       0.407        0.559

ANSWER: 0.585


 5.  What percentage of the variability in the annual rental income is accounted for by the value of the house?

A.  58.5%

B.  41.5%

C.  76.5%

D.  None of the above answers are correct

Enter letter corresponding to correct answer

ANSWER: 58.5%



Question 4

The World Bank collected data on the percentage of GDP that a country spends on health expenditures ("Health expenditure," 2013) and also the percentage of women receiving prenatal care ("Pregnant woman receiving," 2013).  The data for the 15 countries where this information are available for the year 2011 is in the table below:

Health Expenditure (% of GDP)

Prenatal Care (%)

9.6

47.9

3.7

54.6

5.2

93.7

5.2

84.7

10.0

100.0

4.7

42.5

4.8

96.4

6.0

77.1

5.4

58.3

4.8

95.4

4.1

78.0

6.0

93.3

9.5

93.3

6.8

93.7

6.1

89.8

 

1.  Determine the correlation between variables (if it exists) in this relation.  Which variable is the dependent (output) variable?

A.  Percent of women receiving prenatal care

B.  Percent of gross domestic product (GDP) spent on healthcare

Enter letter corresponding to correct answer

ANSWER: A

 2.  Using technology, determine coefficient of correlation r

Enter r value to nearest ten-thousandth, with its sign (no spaces).  Examples of correctly entered responses:

+0.7789         -0.4529       +0.9976

Correlation coefficient calculator:

Correlation and Linear Regression Calculator Applet

ANSWER: +0.1715



 3.  What type of linear correlation does the calculated r value indicate?

A.  Weak negative correlation

B.  Weak positive correlation

C.  No linear correlation

D.  None of the above are correct

Enter letter corresponding to correct answer

ANSWER: B

 4.  Use the correlation coefficient r to find the coefficient of determination r2

Enter answer to nearest ten-thousandth.  Examples of correctly entered responses:

0.9566       0.4070        0.5590

ANSWER: 0.0294



 5.  What percentage of the variability in the percentage of women receiving prenatal care is accounted for by the percentage of GDP spent on healthcare?

A.  17.15%

B.  97.06%

C.  2.94%

D.  None of the above answers are correct

Enter letter corresponding to correct answer

ANSWER: C



Question 5

The table below contains the value of the house and the amount of rental income in a year that the house brings in ("Capital and rental," 2013). 

Table:  Data of House Value versus Rental

Value

Rental

Value

Rental

Value

Rental

Value

Rental

81000

6656

77000

4576

75000

7280

67500

6864

95000

7904

94000

8736

90000

6240

85000

7072

121000

12064

115000

7904

110000

7072

104000

7904

135000

8320

130000

9776

126000

6240

125000

7904

145000

8320

140000

9568

140000

9152

135000

7488

165000

13312

165000

8528

155000

7488

148000

8320

178000

11856

174000

10400

170000

9568

170000

12688

200000

12272

200000

10608

194000

11232

190000

8320

214000

8528

208000

10400

200000

10400

200000

8320

240000

10192

240000

12064

240000

11648

225000

12480

289000

11648

270000

12896

262000

10192

244500

11232

325000

12480

310000

12480

303000

12272

300000

12480

Test at the 5% level for a positive correlation between house value and rental amount.  

(i)  Which of the following statements correctly define both the null hypothesis HO and the alternate hypothesis HA ?

A.     HO :  ρ > 0     HA :  ρ = 0

B.     HO :  ρ = 0     HA :  ρ > 0

C.     HO :  ρ = 0     HA :  ρ < 0

D.     none of these answers are correct

ANSWER: B

 (ii)  Enter the level of significance α used for this test, and the degrees of freedom df:

Enter level of significance in decimal form to nearest hundredth, followed by comma, followed by degrees of freedom value to nearest integer.  Do not enter spaces. 

Examples of correctly entered answers:  0.01,4    0.02,11    0.05,13    0.10,46

ANSWER: 0.05, 46

 (iii)   Use technology to determine correlation coefficient r between independent variable (house value) and dependent variable (annual rental income)

Enter in decimal form to nearest ten-thousandth with sign (positive or negative).  Examples of correctly entered answers: 

-0.0001    +0.0020    -0.0500    +0.3000    +0.7115

Recommended online calculator:

Correlation and Linear Regression Calculator Applet

ANSWER: +0.7647


 (iv)  Calculate and enter test statistic

Enter value in decimal form rounded to nearest hundredth, with appropriate sign (no spaces).  Examples of correctly entered answers:

–2.10      –0.07        +0.60        +1.09

Recommended online calculators:

Correlation Coefficient - Testing Significance

ANSWER: +8.05


 (v)  Using tables, calculator, or spreadsheet:  Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest thousandth.  Examples of correctly entered answers:

0.000     0.001     0.030     0.600      0.814      1.000

Recommended online calculator:

Correlation Coefficient - Testing Significance

ANSWER: 0.000

 (vi)  Comparing p-value and α value, which is the correct decision to make for this hypothesis test? 

A.  Reject Ho

B.  Fail to reject Ho

C.  Accept Ho

D.  Accept HA

Enter letter corresponding to correct answer.

 ANSWER: A

 (vii)  Select the statement that most correctly interprets the result of this test:

A.  The result is statistically significant at .05 level of significance.  Evidence supports the claim that there is a positive correlation between house value and rental amount.

B.  The result is statistically significant at .05 level of significance.  There is not enough evidence to show that there is a positive correlation between house value and rental amount.

C.  The result is not statistically significant at .05 level of significance.  Evidence supports the claim that there is a positive correlation between house value and rental amount.

D.  The result is not statistically significant at .05 level of significance.   There is not enough evidence to show that there is a positive correlation between house value and rental amount.

Enter letter corresponding to most correct answer

ANSWER: A


Question 6

The World Bank collected data on the percentage of GDP that a country spends on health expenditures ("Health expenditure," 2013) and also the percentage of women receiving prenatal care ("Pregnant woman receiving," 2013).  The data for 14 countries where this information is available for the year 2011 are in following table (note: outlier data has been removed):

Data of Health Expenditure versus Prenatal Care

Health Expenditure (% of GDP)

Prenatal Care (%)

3.7

54.6

5.2

93.7

5.2

84.7

10.0

100.0

4.7

42.5

4.8

96.4

6.0

77.1

5.4

58.3

4.8

95.4

4.1

78.0

6.0

93.3

9.5

93.3

6.8

93.7

6.1

89.8

 

Test at the 5% level for a correlation between percentage spent on health expenditure and the percentage of women receiving prenatal care.  

(i)  Which of the following statements correctly define both the null hypothesis HO and the alternate hypothesis HA ?

A.     HO :  ρ = 0     HA :  ρ < 0

B.     HO :  ρ > 0     HA :  ρ = 0

C.     HO :  ρ = 0     HA :  ρ≠0

D.     none of these answers are correct

ANSWER: C

 (ii)  Enter the level of significance α used for this test, and the degrees of freedom df:

Enter level of significance in decimal form to nearest hundredth, followed by comma, followed by degrees of freedom value to nearest integer.  Do not enter spaces. 

Examples of correctly entered answers:  0.01,4    0.02,11    0.05,13    0.10,46

ANSWER: 0.05, 12

 (iii)   Use technology to determine correlation coefficient r between independent variable (percent GDP spent on healthcare) and dependent variable (percent women receiving prenatal care)

Enter in decimal form to nearest ten-thousandth with sign.  Examples of correctly entered answers: 

-0.0001    +0.0020    -0.0500    +0.3000    +0.7115

Recommended online calculator:

Correlation and Linear Regression Calculator Applet

ANSWER: + 0.1715


 (iv)  Calculate and enter test statistic

Enter value in decimal form rounded to nearest hundredth, with appropriate sign (no spaces).  Examples of correctly entered answers:

–2.10      –0.07        +0.60        +1.09

Recommended online calculator:

Correlation Coefficient - Testing Significance

ANSWER: + 0.60


 (v)  Using tables, calculator, or spreadsheet:  Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest thousandth.  Examples of correctly entered answers:

0.000     0.001     0.030     0.600      0.814      1.000

Recommended online calculator:

Correlation Coefficient - Testing Significance

ANSWER: 0.558

 (vi)  Comparing p-value and α value, which is the correct decision to make for this hypothesis test? 

A.  Reject Ho

B.  Fail to reject Ho

C.  Accept Ho

D.  Accept HA

Enter letter corresponding to correct answer.

ANSWER: B

 (vii)  Select the statement that most correctly interprets the result of this test:

A.  The result is statistically significant at .05 level of significance.  Evidence supports the claim that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

B.  The result is statistically significant at .05 level of significance.  There is not enough evidence to show that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

C.  The result is not statistically significant at .05 level of significance.  Evidence supports the claim that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

D.  The result is not statistically significant at .05 level of significance.   There is not enough evidence to show that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

Enter letter corresponding to most correct answer

ANSWER: D

Question 7

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day ("Activities of dolphin," 2013).  The numbers in table below represent the number of groups of dolphins that were partaking in an activity at certain times of days:

Table: Dolphin Activity

 

Activity

Period

Row

Total

Morning

Noon

Afternoon

Evening

Travel

6

6

14

13

39

Feed

28

4

0

56

88

Social

38

5

9

10

62

Column Total

72

15

23

79

189

Is there enough evidence to show that the activity and the time period are independent for dolphins?  Test at the 1% level.

(i)  Which of the following statements correctly defines the null hypothesis HO?

A.  the activity for dolphins is independent of the time period 

B.  the activity for dolphins is not independent of the time period

C.  neither of these statements is correct for HO

Enter letter corresponding to correct answer

ANSWER: A

 (ii)  Which of the following statements correctly defines the alternate hypothesis HA?

A.  the activity for dolphins is independent of the time period 

B.  the activity for dolphins is not independent of the time period

C.  neither of these statements is correct for HA

Enter letter corresponding to correct answer

ANSWER: B

 (iii)  Enter the level of significance α used for this test:

Enter in decimal form.  Examples of correctly entered answers:  0.01    0.02    0.05    0.10

ANSWER: 0.01

  (iv)  Are any of the expected frequency values (for which HO is true) for any cell in your table less than 5?  Calculate the expected frequencies using technology, the select most correct answer:

A.  yes - this will not affect results of hypothesis test

B.  yes - this may invalidate results of hypothesis test

C.  no - this will not affect results of hypothesis test

D.  no - this may invalidate results of hypothesis test

Enter letter corresponding to correct answer.  Recommend using the following applet ( Chi-Square Test of Independence Applet) to create contingency table of expected and observed frequency values in order to answer this question.

ANSWER: B

 (v)  Using calculator, spreadsheet, or online calculator, determine test statistic:

Enter value in decimal form rounded to nearest thousandth.  Examples of correctly entered answers:

2.010         0.307        1.600        11.019

Recommended online calculator:  Chi-Square Test of Independence Applet

ANSWER: 68.465

 (vi)  Using tables, calculator, or spreadsheet:  Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest ten-thousandth.  Examples of correctly entered answers:

0.0001     0.0021     0.0305     0.6004      0.8143     1.0000

Recommended online calculator:  Chi-Square Test of Independence Applet

ANSWER: 0.0000

 (vii)  Comparing p-value and α value, which is the correct decision to make for this hypothesis test? 

A.  Reject Ho

B.  Fail to reject Ho

C.  Accept Ho

D.  Accept HA

Enter letter corresponding to correct answer.

ANSWER: A

  (viii)  Select the statement that most correctly interprets the result of this test:

A.  The result is not statistically significant at .01 level of significance.  Sufficient evidence exists to support the claim that the activity and the time period are NOT independent for dolphins.

B.  The result is not statistically significant at .01 level of significance.  There is not enough evidence to support the claim that the activity and the time period are NOT independent for dolphins.

C.  The result is statistically significant at .01 level of significance.  There is not enough evidence to support the claim that the activity and the time period are NOT independent for dolphins.

D.  The result is statistically significant at .01 level of significance.  Sufficient evidence exists to support the claim that the activity and the time period are NOT independent for dolphins.

Enter letter corresponding to most correct answer

ANSWER: D



Question 8

A person’s educational attainment and age group was collected by the U.S. Census Bureau in 1984 to see if age group and educational attainment are related.  The counts in thousands are in following table ("Education by age," 2013):

Table: Educational Attainment and Age Group

 

Education

Age Group

Row Total

25-34

35-44

45-54

55-64

>64

Did not complete HS

5416

5030

5777

7606

13746

37575

Competed HS

16431

1855

9435

8795

7558

44074

College 1-3 years

8555

5576

3124

2524

2503

22282

College 4 or more years

9771

7596

3904

3109

2483

26863

Column Total

40173

20057

22240

22034

26290

130794

Do the data show that educational attainment and age are independent?  Test at the 5% level.

(i)  Which of the following statements correctly defines the null hypothesis HO?

A.  level of educational attainment is not independent of age 

B.  level of educational attainment is independent of age

C.  neither of these statements is correct for HO

Enter letter corresponding to correct answer

ANSWER: B

 (ii)  Which of the following statements correctly defines the alternate hypothesis HA?

A.  level of educational attainment is not independent of age 

B.  level of educational attainment is independent of age

C.  neither of these statements is correct for HO

Enter letter corresponding to correct answer

ANSWER: A

 (iii)  Enter the level of significance α used for this test:

Enter in decimal form.  Examples of correctly entered answers:  0.01    0.02    0.05    0.10

ANSWER: 0.05

  (iv)  Are any of the expected frequency values (for which HO is true) for any cell in your table less than 5?  Calculate the expected frequencies using technology, the select most correct answer:

A.  yes - this will not affect results of hypothesis test

B.  yes - this may invalidate results of hypothesis test

C.  no - this will not affect results of hypothesis test

D.  no - this may invalidate results of hypothesis test

Enter letter corresponding to correct answer.  Recommend using (Chi-Square Test of Independence Applet) to create contingency table of expected and observed frequency values in order to answer this question.

ANSWER: C

 (v)  Using calculator, spreadsheet, or online calculator, determine test statistic:

Enter value to nearest integer. 

Recommended online calculator:  Chi-Square Test of Independence Applet

ANSWER: 22374

 (vi)  Using tables, calculator, or spreadsheet:  Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest ten-thousandth.  Examples of correctly entered answers:

0.0001     0.0021     0.0305     0.6004      0.8143     1.0000

Recommended online calculator:  Chi-Square Test of Independence Applet

ANSWER: 0.0000

 (vii)  Comparing p-value and α value, which is the correct decision to make for this hypothesis test? 

A.  Accept Ho

B.  Accept HA

C.  Reject Ho

D.  Fail to reject Ho

Enter letter corresponding to correct answer.

ANSWER: C

  (viii)  Select the statement that most correctly interprets the result of this test:

A.  The result is statistically significant at .05 level of significance.  There is not enough evidence to support the claim that level of educational attainment and age are NOT independent.

B.  The result is statistically significant at .05 level of significance.  Sufficient evidence exists to support the claim that level of educational attainment and age are NOT independent.

C.  The result is not statistically significant at .05 level of significance.  Sufficient evidence exists to support the claim that level of educational attainment and age are NOT independent.

D.  The result is not statistically significant at .05 level of significance.  There is not enough evidence to support the claim that level of educational attainment and age are NOT independent.

Enter letter corresponding to most correct answer

ANSWER: B



Question 9

In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in the table below ("Global health observatory," 2013).  In addition, the proportion of deaths of females from all causes for the same age groups are also in table below. 

Table: Deaths of Females for Different Age Groups

Age

5-14

15-29

30-49

50-69

Total

Cardiovascular Frequency

8

16

56

433

513

All Cause Proportion

0.10

0.12

0.26

0.52

 

Do the data show that the death from cardiovascular disease are in the same proportion as all deaths for the different age groups?  Test at the 5% level.

(i)  Which of the following statements correctly defines the null hypothesis HO?

A.  Deaths from cardiovascular disease in females are not in the same proportion as all deaths for the different age groups

B.  Deaths from cardiovascular disease in females are in the same proportion as all deaths for the different age groups

C.  neither of these statements is correct for HO

Enter letter corresponding to correct answer

ANSWER: B

 (ii)  Which of the following statements correctly defines the alternate hypothesis HA?

A.  Deaths from cardiovascular disease in females are in the same proportion as all deaths for the different age groups

B.  Deaths from cardiovascular disease in females are not in the same proportion as all deaths for the different age groups

C.  neither of these statements is correct for HA

Enter letter corresponding to correct answer

ANSWER: B

 (iii)  Enter the level of significance α used for this test:

Enter in decimal form.  Examples of correctly entered answers:  0.01    0.02    0.05    0.10

ANSWER: 0.05

  (iv)  Are any of the expected frequency values (for which HO is true) for any cell in your table less than 5?  Calculate the expected frequencies using technology, the select most correct answer:

A.  yes - this will not affect results of hypothesis test

B.  yes - this may invalidate results of hypothesis test

C.  no - this will not affect results of hypothesis test

D.  no - this may invalidate results of hypothesis test

Enter letter corresponding to correct answer.  Recommend using (Chi-Square Goodness-of-Fit Applet) to create contingency table of expected and observed frequency values in order to answer this question.  BE SURE when entering expected frequency data you select what format you're entering the data ("percent expected", "fraction expected" which includes decimal, or "actual number expected").

ANSWER: C

 (v)  Using calculator, spreadsheet, or online calculator, determine test statistic:

Enter value in decimal form rounded to nearest thousandth.  Examples of correctly entered answers:

2.010         0.307        1.600        11.019

Recommended online calculator:  Chi-Square Goodness-of-Fit Applet

BE SURE when entering expected frequency data you select what format you're entering the data ("percent expected", "fraction expected" which includes decimal, or "actual number expected").

ANSWER: 218.756

 (vi)  Using tables, calculator, or spreadsheet:  Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest ten-thousandth.  Examples of correctly entered answers:

0.0001     0.0021     0.0305     0.6004      0.8143     1.0000

Recommended online calculator:  Chi-Square Goodness-of-Fit Applet

BE SURE when entering expected frequency data you select what format you're entering the data ("percent expected", "fraction expected" which includes decimal, or "actual number expected").

ANSWER: 0.0000

 (vii)  Comparing p-value and α value, which is the correct decision to make for this hypothesis test? 

A.  Reject Ho

B.  Fail to reject Ho

C.  Accept Ho

D.  Accept HA

Enter letter corresponding to correct answer.

ANSWER: A

  (viii)  Select the statement that most correctly interprets the result of this test:

A.  The result is not statistically significant at .05 level of significance.  Sufficient evidence exists to support the claim that deaths from cardiovascular disease in females are not in the same proportion as all deaths of females for the different age groups.

B.  The result is statistically significant at .05 level of significance.  Sufficient evidence exists to support the claim that deaths from cardiovascular disease in females are not in the same proportion as all deaths of females for the different age groups.

C.  The result is not statistically significant at .05 level of significance.  There is not enough evidence to support the claim that deaths from cardiovascular disease in females are not in the same proportion as all deaths of females for the different age groups.

D.  The result is statistically significant at .05 level of significance.  There is not enough evidence to support the claim  that deaths from cardiovascular disease in females are not in the same proportion as all deaths of females for the different age groups.

Enter letter corresponding to most correct answer

ANSWER: B



Question 10

A six-sided die is rolled 120 times (results listed in table below). 

Face Value

Frequency

1

15

2

29

3

16

4

15

5

30

6

15

 

Determine if the die is fair (if it is fair, what is the expected frequency of each face value through 120 rolls?).  Test at the 1% level.

(i)  Which of the following statements correctly defines the null hypothesis HO?

A.  Distribution of observed die rolls DOES NOT FIT expected distribution of die rolls (≠)

B.  Distribution of observed die rolls FITS expected distribution of die rolls (=)

C.  neither of these statements is correct for HO

Enter letter corresponding to correct answer

ANSWER:B


 (ii)  Which of the following statements correctly defines the alternate hypothesis HA?

A.  Distribution of observed die rolls DOES NOT FIT expected distribution of die rolls (≠)

B.  Distribution of observed die rolls FITS expected distribution of die rolls (=)

C.  neither of these statements is correct for HA

Enter letter corresponding to correct answer

ANSWER: A

 (iii)  Enter the level of significance α used for this test:

Enter in decimal form.  Examples of correctly entered answers:  0.01    0.02    0.05    0.10

ANSWER: 0.01


  (iv)  Are any of the expected frequency values (for which HO is true) for any cell in your table less than 5?  You'll have to create the expected frequency for each value in order to select most correct answer:

A.  no - this will not affect results of hypothesis test

B.  no - this may invalidate results of hypothesis test

C.  yes - this will not affect results of hypothesis test

D.  yes - this may invalidate results of hypothesis test

Enter letter corresponding to correct answer. 

ANSWER: B


 (v)  Using calculator, spreadsheet, or online calculator, determine test statistic:

Enter value in decimal form rounded to nearest thousandth.  Examples of correctly entered answers:

2.010         0.307        1.600        11.019

Recommended online calculator:  Chi-Square Goodness-of-Fit Applet

BE SURE when entering expected frequency data you select what format you're entering the data ("percent expected", "fraction expected" which includes decimal, or "actual number expected").

ANSWER: 13.600


 (vi)  Using tables, calculator, or spreadsheet:  Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest ten-thousandth.  Examples of correctly entered answers:

0.0001     0.0021     0.0305     0.6004      0.8143     1.0000

Recommended online calculator:  Chi-Square Goodness-of-Fit Applet

BE SURE when entering expected frequency data you select what format you're entering the data ("percent expected", "fraction expected" which includes decimal, or "actual number expected").

ANSWER: 0.0184


 (vii)  Comparing p-value and α value, which is the correct decision to make for this hypothesis test? 

A.  Reject Ho

B.  Fail to reject Ho

C.  Accept Ho

D.  Accept HA

Enter letter corresponding to correct answer.

ANSWER: B


(viii)  Select the statement that most correctly interprets the result of this test:

A.  The result is not statistically significant at .01 level of significance.  Sufficient evidence exists to support the claim that distribution of observed rolls of the die does NOT fit the distribution of expected rolls.  There is sufficient evidence to support the hypothesis that the die is NOT fair.

B.  The result is statistically significant at .01 level of significance.  Sufficient evidence exists to support the claim that distribution of observed rolls of the die does NOT fit the distribution of expected rolls.  There is sufficient evidence to support the hypothesis that the die is NOT fair.

C.  The result is not statistically significant at .01 level of significance.  There is not enough evidence to support the claim that distribution of observed rolls of the die does NOT fit the distribution of expected rolls.  There is insufficient evidence to support the hypothesis that the die is NOT fair.

D.  The result is statistically significant at .01 level of significance.  There is not enough evidence to support the claim that distribution of observed rolls of the die does NOT fit the distribution of expected rolls.  There is insufficient evidence to support the hypothesis that the die is NOT fair.

Enter letter corresponding to most correct answer

ANSWER: C




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