Stat 200 Week 7 homework problems (A+ Solutions)

Stat 200 Week 7 homework problems (A+ Solutions)
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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

ValueRentalValueRentalValueRentalValueRental
810006656770004576750007280675006864
950007904940008736900006240850007072
12100012064115000790411000070721040007904
1350008320130000977612600062401250007904
1450008320140000956814000091521350007488
16500013312165000852815500074881480008320
1780001185617400010400170000956817000012688
2000001227220000010608194000112321900008320
214000852820800010400200000104002000008320
24000010192240000120642400001164822500012480
28900011648270000128962620001019224450011232
32500012480310000124803030001227230000012480

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 (%)
9.647.9
3.754.6
5.293.7
5.284.7
10.0100.0
4.742.5
4.896.4
6.077.1
5.458.3
4.895.4
4.178.0
6.093.3
9.593.3
6.893.7
6.189.8

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

ValueRentalValueRentalValueRentalValueRental
810006656770004576750007280675006864
950007904940008736900006240850007072
12100012064115000790411000070721040007904
1350008320130000977612600062401250007904
1450008320140000956814000091521350007488
16500013312165000852815500074881480008320
1780001185617400010400170000956817000012688
2000001227220000010608194000112321900008320
214000852820800010400200000104002000008320
24000010192240000120642400001164822500012480
28900011648270000128962620001019224450011232
32500012480310000124803030001227230000012480

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 (%)
9.647.9
3.754.6
5.293.7
5.284.7
10.0100.0
4.742.5
4.896.4
6.077.1
5.458.3
4.895.4
4.178.0
6.093.3
9.593.3
6.893.7
6.189.8

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

ValueRentalValueRentalValueRentalValueRental
810006656770004576750007280675006864
950007904940008736900006240850007072
12100012064115000790411000070721040007904
1350008320130000977612600062401250007904
1450008320140000956814000091521350007488
16500013312165000852815500074881480008320
1780001185617400010400170000956817000012688
2000001227220000010608194000112321900008320
214000852820800010400200000104002000008320
24000010192240000120642400001164822500012480
28900011648270000128962620001019224450011232
32500012480310000124803030001227230000012480

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 (%)
9.647.9
3.754.6
5.293.7
5.284.7
10.0100.0
4.742.5
4.896.4
6.077.1
5.458.3
4.895.4
4.178.0
6.093.3
9.593.3
6.893.7
6.189.8

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

PeriodRow

Total

MorningNoonAfternoonEvening
Travel66141339
Feed28405688
Social38591062
Column Total72152379189

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 GroupRow Total
25-3435-4445-5455-64>64
Did not complete HS54165030577776061374637575
Competed HS16431185594358795755844074
College 1-3 years8555557631242524250322282
College 4 or more years9771759639043109248326863
Column Total4017320057222402203426290130794

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

Age5-1415-2930-4950-69Total
Cardiovascular Frequency81656433513
All Cause Proportion0.100.120.260.521

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

SafetyReliabilityCostPerformanceComfortLooks
846246344727

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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