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 persons 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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