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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 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.