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STAT 200 Week 7 Homework Solutions

STAT 200 Week 7 Homework Problems

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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

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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

10400

0

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

8

4.7

 

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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