statistics ques
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 woman 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 woman receiving prenatal care. Then use the regression equation to find the percent of woman 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 Heath 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 |
For each problem, state the random variables. Also, look to see if there are any outliers that need to be removed. Do the correlation analysis with and without the suspected outlier points to determine if their removal affects the correlation. The data sets in this section are in section 10.1.
10.2.2
Table #10.1.6 (from problem 10.1.2) 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.
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 woman 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 (from problem 10.1.4). Find the correlation coefficient and coefficient of determination and then interpret both.
For each problem, state the random variables. The data sets in this section are in the homework for section 10.1 and were also used in section 10.2. If you removed any data points as outliers in the other sections, remove them in this sections homework too.
10.3.2
Table #10.1.6 (from problem 10.1.2) contains the value of the house and the amount of rental income in a year that the house brings in (“Capital and rental,” 2013).
a.) Test at the 5% level for a positive correlation between house value and rental amount.
b.) Find the standard error of the estimate.
c.) Compute a 95% prediction interval for the rental income on a house worth $230,000.
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 woman 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 (from problem 10.1.4).
a.) Test at the 5% level for a correlation between percentage spent on health expenditure and the percentage of woman receiving prenatal care.
b.) Find the standard error of the estimate.
c.) Compute a 95% prediction interval for the percentage of woman receiving prenatal care for a country that spends 5.0 % of GDP on health expenditure.
In each problem show all steps of the hypothesis test. If some of the assumptions are not met, note that the results of the test may not be correct and then continue the process of the hypothesis test.
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 |
|
Completed HS |
16431 |
1855 |
9435 |
8795 |
7558 |
44074 |
|
College 1-3 year |
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 |
In each problem show all steps of the hypothesis test. If some of the assumptions are not met, note that the results of the test may not be correct and then continue the process of the hypothesis test.
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 reason for choosing a car are equally likely? Test at the 5% level.
