## Data of House Value versus Rental

**Homework Questions**

**Please provide work on an excel sheet for each problem. Be sure to put answers on this document too.**

**Problem # 1 **

**Problem # 1:**

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 |

**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*

**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*:

**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*

**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*

**Which rental income that you calculated do you think is closer to the true rental income?**- $10884, since house value producing this annual rental income would fall within range of house value data (rental income value is interpolated)
- Both calculations are equally accurate since they are calculated using the same regression equation
- $14964, since annual rental income is extrapolated

*Enter letter corresponding to correct answer*

**Problem# 2 **

#2:

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 |

**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*

**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*:

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

*Enter amount to nearest thousandth; do not include percent sign*

**Use the regression equation to find the percent of women receiving prenatal care for a country that spends 12.0% of GDP on health expenditure**

*Enter amount to nearest thousandth; do not include percent sign*

**Which prenatal care percentage that you calculated do you think is closer to the true percentage?**- 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)
- Both calculations are equally accurate since they are calculated using the same regression equation
- 89.670, since data for percentage of women receiving prenatal care is extrapolated

*Enter letter corresponding to correct answer*

**Problem# 3**

Problem# 3 options:

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 |

**Determine the correlation between variables (if it exists) in this relation. Which variable is the dependent (output) variable?****Value of house****Annual rental income generated**

*Enter letter corresponding to correct answer*

**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*:

**What type of linear correlation does the calculated***r*value indicate?**Strong positive correlation****Moderate positive correlation****Weak negative correlation****No linear correlation****None of the above are correct**

*Enter letter corresponding to correct answer*

**Use the correlation coefficient***r*to find the coefficient of determination*r*^{2}

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

0.956 0.407 0.559

**What percentage of the variability in the annual rental income is accounted for by the value of the house?****58.5%****41.5%****76.5%****None of the above answers are correct**

*Enter letter corresponding to correct answer*

**Problem# 4 **

Problem# 4 options:

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 |

**Determine the correlation between variables (if it exists) in this relation. Which variable is the dependent (output) variable?****Percent of women receiving prenatal care****Percent of gross domestic product (GDP) spent on healthcare**

*Enter letter corresponding to correct answer*

**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*:

**What type of linear correlation does the calculated***r*value indicate?**Weak negative correlation****Weak positive correlation****No linear correlation****None of the above are correct**

*Enter letter corresponding to correct answer*

**Use the correlation coefficient***r*to find the coefficient of determination*r*^{2}

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

0.9566 0.4070 0.5590

**What percentage of the variability in the percentage of women receiving prenatal care is accounted for by the percentage of GDP spent on healthcare?****17.15%****97.06%****2.94%****None of the above answers are correct**

*Enter letter corresponding to correct answer*

**Problem# 5**

** **

Problem# 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 H_{O} and the alternative hypothesis H_{A} ?**

*H*:_{O}*ρ*> 0*H*:_{A}*ρ*= 0*H*:_{O}*ρ*= 0*H*:_{A}*ρ*> 0*H*:_{O}*ρ*= 0*H*:_{A}*ρ*< 0**none of these answers are correct**

** (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

** **

** (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:

* ***(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:

* ***(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:

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

**Reject***H*_{o}**Fail to reject***H*_{o}**Accept***H*_{o}**Accept***H*_{A}

*Enter letter corresponding to correct answer.*

** **

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

**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.****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.****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.****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*

**Problem #6**

Problem #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 H_{O} and the alternative hypothesis H_{A} ?**

*H*:_{O}*ρ*= 0*H*:_{A}*ρ*< 0*H*:_{O}*ρ*> 0*H*:_{A}*ρ*= 0*H*:_{O}*ρ*= 0*H*:_{A}*ρ*≠ 0**none of these answers are correct**

** (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

** **

** (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:

* ***(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:

* ***(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:

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

**Reject***H*_{o}**Fail to reject***H*_{o}**Accept***H*_{o}**Accept***H*_{A}

*Enter letter corresponding to correct answer.*

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

**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.****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.****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.****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*

** **

**Problem# 7 **

Problem 7 options:

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 H_{O}?**

**the activity for dolphins is independent of the time period****the activity for dolphins is not independent of the time period****neither of these statements is correct for***H*_{O}

*Enter letter corresponding to correct answer*

** (ii) Which of the following statements correctly defines the alternative hypothesis H_{A}?**

**the activity for dolphins is independent of the time period****the activity for dolphins is not independent of the time period****neither of these statements is correct for***H*_{A}

*Enter letter corresponding to correct answer*

** (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

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

**yes – this will not affect results of hypothesis test****yes – this may invalidate results of hypothesis test****no – this will not affect results of hypothesis test****no – this may invalidate results of hypothesis test**

** (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

** (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:

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

**Reject***H*_{o}**Fail to reject***H*_{o}**Accept***H*_{o}**Accept***H*_{A}

*Enter letter corresponding to correct answer.*

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

**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.****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.****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.****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*

**Problem #8**

Problem# 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 H_{O}?**

**level of educational attainment is not independent of age****level of educational attainment is independent of age****neither of these statements is correct for***H*_{O}

*Enter letter corresponding to correct answer*

** (ii) Which of the following statements correctly defines the alternative hypothesis H_{A}?**

**level of educational attainment is not independent of age****level of educational attainment is independent of age****neither of these statements is correct for***H*_{O}

*Enter letter corresponding to correct answer*

** (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

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

**yes – this will not affect results of hypothesis test****yes – this may invalidate results of hypothesis test****no – this will not affect results of hypothesis test****no – this may invalidate results of hypothesis test**

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

*Enter value to nearest integer. *

** (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

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

**Accept***H*_{o}**Accept***H*_{A}**Reject***H*_{o}**Fail to reject***H*_{o}

*Enter letter corresponding to correct answer.*

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

**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.****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.****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.****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*

**Problem# 9**

Problem# 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 H_{O}?**

**Deaths from cardiovascular disease in females are not in the same proportion as all deaths for the different age groups****Deaths from cardiovascular disease in females are in the same proportion as all deaths for the different age groups****neither of these statements is correct for***H*_{O}

*Enter letter corresponding to correct answer*

** (ii) Which of the following statements correctly defines the alternative hypothesis H_{A}?**

**Deaths from cardiovascular disease in females are in the same proportion as all deaths for the different age groups****Deaths from cardiovascular disease in females are not in the same proportion as all deaths for the different age groups****neither of these statements is correct for***H*_{A}

*Enter letter corresponding to correct answer*

** (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

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

**yes – this will not affect results of hypothesis test****yes – this may invalidate results of hypothesis test****no – this will not affect results of hypothesis test****no – this may invalidate results of hypothesis test**

** (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

** (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

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”).

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

**Reject***H*_{o}**Fail to reject***H*_{o}**Accept***H*_{o}**Accept***H*_{A}

*Enter letter corresponding to correct answer.*

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

**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.****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.****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.****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*

**Problem# 10**

Problem 10 options:

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 H_{O}?**

**Distribution of observed die rolls DOES NOT FIT expected distribution of die rolls (≠)****Distribution of observed die rolls FITS expected distribution of die rolls (=)****neither of these statements is correct for***H*_{O}

*Enter letter corresponding to correct answer*

** (ii) Which of the following statements correctly defines the alternative hypothesis H_{A}?**

**Distribution of observed die rolls DOES NOT FIT expected distribution of die rolls (≠)****Distribution of observed die rolls FITS expected distribution of die rolls (=)****neither of these statements is correct for***H*_{A}

*Enter letter corresponding to correct answer*

** (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

**(iv) Are any of the expected frequency values (for which H_{O} 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:**

**no – this will not affect results of hypothesis test****no – this may invalidate results of hypothesis test****yes – this will not affect results of hypothesis test****yes – this may invalidate results of hypothesis test**

*Enter letter corresponding to correct answer. *

** (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

0.0001 0.0021 0.0305 0.6004 0.8143 1.0000

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

**Reject***H*_{o}**Fail to reject***H*_{o}**Accept***H*_{o}**Accept***H*_{A}

*Enter letter corresponding to correct answer.*

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

**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.****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.****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.****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*