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 81000 6656 77000 4576 75000 95000 7904 94000 8736 90000 121000 12064 115000 7904 110000 135000 8320 130000 9776 126000 145000 8320 140000 9568 140000 165000 13312 165000 8528 155000 178000 11856 174000 10400 170000 200000 12272 200000 10608 194000 214000 8528 208000 10400 200000 240000 10192 240000 12064 240000 289000 11648 270000 12896 262000 325000 12480 310000 12480 303000 Rental 7280 6240 7072 6240 9152 7488 9568 11232 10400 11648 10192 12272 Value 67500 85000 104000 125000 135000 148000 170000 190000 200000 225000 244500 300000 Rental 6864 7072 7904 7904 7488 8320 12688 8320 8320 12480 11232 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 Prenatal Expenditure Care (%) (% of GDP) 9.6 47.9 54.6 3.7 93.7 5.2 84.7 5.2 100.0 10.0 4.7 4.8 6.0 5.4 4.8 4.1 6.0 9.5 6.8 6.1 42.5 96.4 77.1 58.3 95.4 78.0 93.3 93.3 93.7 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 81000 6656 77000 4576 75000 95000 7904 94000 8736 90000 121000 12064 115000 7904 110000 135000 8320 130000 9776 126000 145000 8320 140000 9568 140000 165000 13312 165000 8528 155000 178000 11856 174000 10400 170000 200000 12272 200000 10608 194000 214000 8528 208000 10400 200000 240000 10192 240000 12064 240000 289000 11648 270000 12896 262000 325000 12480 310000 12480 303000 Rental 7280 6240 7072 6240 9152 7488 9568 11232 10400 11648 10192 12272 Value 67500 85000 104000 125000 135000 148000 170000 190000 200000 225000 244500 300000 Rental 6864 7072 7904 7904 7488 8320 12688 8320 8320 12480 11232 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 Prenatal Expenditure Care (%) (% of GDP) 9.6 3.7 5.2 5.2 10.0 4.7 4.8 6.0 5.4 4.8 4.1 6.0 9.5 6.8 6.1 47.9 54.6 93.7 84.7 100.0 42.5 96.4 77.1 58.3 95.4 78.0 93.3 93.3 93.7 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 81000 6656 77000 4576 75000 95000 7904 94000 8736 90000 121000 12064 115000 7904 110000 135000 8320 130000 9776 126000 145000 8320 140000 9568 140000 165000 13312 165000 8528 155000 178000 11856 174000 10400 170000 200000 12272 200000 10608 194000 214000 8528 208000 10400 200000 240000 10192 240000 12064 240000 289000 11648 270000 12896 262000 325000 12480 310000 12480 303000 Rental 7280 6240 7072 6240 9152 7488 9568 11232 10400 11648 10192 12272 Value 67500 85000 104000 125000 135000 148000 170000 190000 200000 225000 244500 300000 Rental 6864 7072 7904 7904 7488 8320 12688 8320 8320 12480 11232 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 Prenatal Expenditure Care (%) (% of GDP) 9.6 47.9 54.6 3.7 93.7 5.2 84.7 5.2 100.0 10.0 42.5 4.7 96.4 4.8 77.1 6.0 58.3 5.4 95.4 4.8 78.0 4.1 93.3 6.0 93.3 9.5 93.7 6.8 89.8 6.1 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 Travel Feed Social Column Total Morning 6 28 38 72 Period Noon Afternoon 6 14 4 0 5 9 15 23 Evening 13 56 10 79 Row Total 39 88 62 189 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 Age Group Education 25-34 35-44 45-54 55-64 Did not 5416 5030 5777 7606 complete HS Competed 16431 1855 9435 8795 HS College 1-3 8555 5576 3124 2524 years College 4 or 9771 7596 3904 3109 more years Column Total 40173 20057 22240 22034 >64 13746 Row Total 37575 7558 44074 2503 22282 2483 26863 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 8 16 56 433 513 Frequency 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 84 Reliability 62 Cost 46 Performance 34 Comfort 47 Looks 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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