STAT 200 Week 7 Homework Solutions

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STAT 200 Week 7 Homework Problems


10.1.2

Table #10.1.6 contains the value of the house and the amount of rental income in a year that the house brings in ("Capital and rental," 2013). Create a scatter plot and find a regression equation between house value and rental income. Then use the regression equation to find the rental income a house worth $230,000 and for a house worth $400,000. Which rental income that you calculated do you think is closer to the true rental income? Why?

Table #10.1.6: 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

10.1.4

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 countries where this information are available for the year 2011 is in table #10.1.8. Create a scatter plot of the data and find a regression equation between percentage spent on health expenditure and the percentage of women receiving prenatal care. Then 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 and for a country that spends 12.0% of GDP. Which prenatal care percentage that you calculated do you think is closer to the true percentage? Why?

Table #10.1.8: Data of Health Expenditure versus Prenatal Care

  

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

10.2.2

Table #10.1.6 contains the value of the house and the amount of rental income in a year that the house brings in ("Capital and rental," 2013). Find the correlation coefficient and coefficient of determination and then interpret both.

Table #10.1.6: 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

10.2.4

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 countries where this information is available for the year 2011 are in table #10.1.8. Find the correlation coefficient and coefficient of determination and then interpret both.

Table #10.1.8: Data of Health Expenditure versus Prenatal Care

  

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

10.3.2

Table #10.1.6 contains the value of the house and the amount of rental income in a year that the house brings in ("Capital and rental," 2013). 

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

Table #10.1.6: 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

10.3.4

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 countries where this information is available for the year 2011 are in table #10.1.8. 

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

Table #10.1.8: Data of Health Expenditure versus Prenatal Care

  

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

11.1.2

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 #11.1.6 represent the number of groups of dolphins that were partaking in an activity at certain times of days. Is there enough evidence to show that the activity and the time period are independent for dolphins? Test at the 1% level.

Table #11.1.6: 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

  

11.1.4

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 table #11.1.8 ("Education by age," 2013). Do the data show that educational attainment and age are independent? Test at the 5% level.

Table #11.1.8: 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

11.2.4

In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in table #11.2.6 ("Global health observatory," 2013). In addition, the proportion of deaths of females from all causes for the same age groups are also in table #11.2.6. 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.

Table #11.2.6: 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


  

11.2.6

A project conducted by the Australian Federal Office of Road Safety asked people many questions about their cars. One question was the reason that a person chooses a given car, and that data is in table #11.2.8 ("Car preferences," 2013). 

Table #11.2.8: Reason for Choosing a Car

  

Safety


Reliability


Cost


Performance


Comfort


Looks

 

84


62


46


34


47


27

Do the data show that the frequencies observed substantiate the claim that the reasons for choosing a car are equally likely? Test at the 5% level.

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