Bivariate data often arises from the use of two different techniques to measure the same quantity. As an example, the accompanying observations on x = hydrogen concentration (ppm) using a gas chromatography method and y = concentration using a new sensor method were read from a graph in the article “A New Method to Measure the Diffusible Hydrogen Content in Steel Weldments Using a Polymer Electrolyte-Bused Hydrogen Sensor” (Welding Res., July 1997: 251s–256s).
x | 47 | 62 | 65 | 70 | 70 | 78 | 95 | 100 | 114 | 118 |
y | 38 | 62 | 53 | 67 | 84 | 79 | 93 | 106 | 117 | 116 |
x | 124 | 127 | 140 | 140 | 140 | 150 | 152 | 164 | 198 | 221 |
y | 127 | 114 | 134 | 139 | 142 | 170 | 149 | 154 | 200 | 215 |
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Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
- The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of fifteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. The least-squares regression line for these data has equation y = 40.63 - 0.46x . This line is shown in the scatter plot below. Mileage, x(in thousands) Used selling price, y(in thousands of dollars) 23.9 29.5 37.6 22.6 20.8 30.9 23.3 33.1 28.3 26.1 27.3 29.9 27.7 29.8 20.9 30.3 25.8 27.2 34.4 25.9 23.9 27.4 23.8 27.5 23.2 31.4 15.6 34.0 29.4 27.7 Send…arrow_forwardManagers of an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y , in dollars) and the maximum temperature (denoted by x , in degrees Fahrenheit) for each of fifteen randomly selected days during the past year are given below. These data are plotted in the scatter plot in Figure 1. Temperature, x(in degrees Fahrenheit) Coffee sales, y(in dollars) 53.1 2215.5 76.6 1982.7 70.1 1937.3 39.7 2251.1 72.5 1603.9 48.4 2024.2 46.7 2135.3 83.9 1536.5 58.4 1965.6 38.5 1944.3 68.2 1746.1 75.4 1472.1 65.6 1819.5 53.9 1627.4 45.1 1782.3 Send data to calculator Send data to Excel Coffee sales(in dollars) y 1200 1400 1600 1800 2000 2200 2400 x 40 50 60 70 80 90…arrow_forwardRecently, researchers have begun to focus on the relationship between potentially toxic environmental exposures in children to a number of adverse health outcomes. Suppose one such researcher wants to investigate the relationship between lead levels in soil (micrograms/dL) and BMI (kg/m2). The following table represents a SRS of households with the corresponding exterior lead levels and BMI of a randomly sampled child in the home. Lead levels BMI 13.6 19.7 14.3 19.9 9.7 20.1 9.4 22.1 11.4 19.8 10.9 21.6 A) Write out the null and alternative hypotheses for a formal test of significance testing the correlation between the two variables and calulate a t statistic and interpret your pvalue and results.arrow_forward
- The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of sixteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. With the aim of predicting the used selling price from the number of miles driven, we might examine the least-squares regression line, Ŷ=42.39-0.52x. This line is shown in the scatter plot below. (The 2nd picture contains the rest of the data as it would not fit in the first pic and it includes the question as well.)arrow_forwardThe Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of sixteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. The least-squares regression line for these data has equation Ŷ=42.80-0.53x. This line is shown in the scatter plot below. (The 2nd picture contains the rest of the data as it would not fit in the first pic and it includes the question as well.)arrow_forwardThe Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. With the aim of predicting the used selling price from the number of miles driven, we might examine the least-squares regression line, =y−41.990.51x . This line is shown in the scatter plot below. Based on the sample data and the regression line, complete the following. (a)For these data, mileages that are less than the mean of the mileages tend to be paired with used selling prices that are ▼(Choose one) the mean of the used selling prices. (b)According to the regression equation, for an increase of…arrow_forward
- Managers of an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y, in dollars) and the maximum temperature (denoted by x, in degrees Fahrenheit) for each of sixteen randomly selected days during the past year are given below. These data are plotted in the scatter plot in Figure 1. Temperature, x(in degrees Fahrenheit) Coffee sales, y(in dollars) 46.6 2141.1 56.9 1923.2 75.4 1990.8 73.1 1677.7 49.0 2012.9 57.3 1593.6 64.7 1855.5 37.1 1997.9 66.5 1744.9 50.9 2227.9 39.7 2241.5 53.3 1779.8 74.7 1527.4 81.3 1521.4 44.7 1792.0 69.3 1942.1 The value of the sample correlation coefficient r for these data is approximately…arrow_forwardManagers of an outdoor coffee stand in Coast City are examing the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y, in dollars) and the maximum temperature (denoted by x, in degrees Fahrenheit) for each of fifteen randomly selected days during the past year are given below. These data are plotted in the scatter plot in Figure 1. The value of the sample correlation coefficient r for these data is approximately −0.649. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places. What is the value of the y-intercept of the least-squares regression…arrow_forwardLow-Birth-Weight Hospital Stays. Data on low-birthweight babies were collected over a 2-year period by 14 participating centers of the National Institute of Child Health and Human Development Neonatal Research Network. Results were reported by J. Lemons et al. in the on-line paper “Very Low Birth Weight Outcomes of the National Institute of ChildHealth and Human Development Neonatal Research Network” (Pediatrics, Vol. 107, No. 1, p. e1). For the 1084 surviving babies whose birth weights were 751– 1000 grams, the average length of stay in the hospital was 86 days, although one center had an average of 66 days and another had an average of 108 days. a. Can the mean lengths of stay be considered population means? Explain your answer.b. Assuming that the population standard deviation is 12 days, determine the z-score for a baby’s length of stay of 86 days at the center where the mean was 66 days.c. Assuming that the population standard deviation is 12 days, determine the z-score for a…arrow_forward
- The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of fifteen Cadets, each bought "new" two years ago and each sold "used" within the past month. For each Cadet in the sample, we have listed both the mileage, x (in thousands), that the Cadet had on its odometer at the time it was sold used, and the price, y (in thousands of dollars), at which the Cadet was sold used. These data are shown graphically in the scatter plot in Figure 1. Mileage, x(in thousands) Used selling price, y(in thousands of dollars) 21.1 31.2 34.2 25.8 23.3 34.1 37.5 22.8 29.1 27.1 24.2 29.7 23.7 28.0 27.7 25.1 24.1 27.6 23.2 30.9 26.7 31.7 28.1 30.0 20.9 31.6 15.2 34.6 25.7 26.6 The least-squares regression line for these data has a slope of approximately −0.5. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as…arrow_forwardThe Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of sixteen Cadets, each bought "new" two years ago and each sold "used" within the past month. For each Cadet in the sample, we have listed both the mileage, x (in thousands), that the Cadet had on its odometer at the time it was sold used, and the price, y (in thousands of dollars), at which the Cadet was sold used. These data are shown graphically in the scatter plot in Figure 1. Also given is the product of the mileage and the used selling price for each of the sixteen Cadets. (These products, written in the column labelled "xy", may aid in calculations.)arrow_forwardA deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of a research paper supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (the treatment group) and a control sample given no supplement, both initially and after a 9-day period. Initial Measurement Treatment Control 11.2 9.1 9.6 8.7 10.1 9.7 8.5 10.8 10.3 10.9 10.6 10.6 11.7 10.1 9.7 12.3 10.8 8.8 10.3 10.4 10.4 10.9 11.2 10.4 9.4 11.6 10.6 10.9 10.7 8.4 After 9 Days Treatment Control 138.3 9.3 104 8.7 96.4 8.7 89 10.1 88 9.6 103.8 8.6 147.3 10.2 97.1 12.2 172.6 9.3 146.3 9.5 99 8.2 122.3 8.9 103 12.5 117.8 9.1 121.5 93 (a) Use the given data for the treatment group to determine if there…arrow_forward
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