Concept explainers
NW Ramp Metering Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the freeway, resulting in a freer flow of cars, which ultimately results in faster travel times. To test whether ramp metering is effective in reducing travel times, engineers in Minneapolis, Minnesota, conducted an experiment in which a section of freeway had ramp meters installed on the on-ramps. The response variable for the study was speed of the vehicles. A random sample of 15 cars on the highway for a Monday at 6 P.M. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 P.M. with the meters off resulted in the following speeds (in miles per hour).
- a. Draw side-by-side boxplots of each data set. Does there appear to be a difference in the speeds? Are there any outliers?
- b. Are the ramp meters effective in maintaining a higher speed on the freeway? Use the α = 0.10 level of significance.
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Fundamentals of Statistics (5th Edition)
- Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.arrow_forwardThe ordered pairs below give the median sales prices y (in thousands of dollars) of new homes sold in a neighborhood from 2009 through 2016. (2009, 179.4) (2011, 191.0) (2013, 202.6) (2015, 214.9) (2010, 185.4) (2012, 196.7) (2014, 208.7) (2016, 221.4) A linear model that approximates the data is y=5.96t+125.5,9t16, where t represents the year, with t=9 corresponding to 2009. Plot the actual data and the model on the same graph. How closely does the model represent the data?arrow_forwardA Professor offered a course that was delivered half online and half in-person (e.g., 1 week online and 1 week in-person). The Professor hypothesized that students were spending less time engaged with course material during online weeks compared to in-person weeks. At the end of the semester, students were asked to provide the amount of time they tended to course tasks in a week. Tasks included doing course readings, preparing lecture material, and doing weekly assignments. The weeks were classified as online or in-person and the average amount of time (rounded to the nearest hour) spent engaged with course material is provided for 15 students in the course. Online 4 3 6 2 2 4 7 4 3 2 6 3 In-person 7 4 4 6 4 3 4 Test the hypothesis at the 5% significance level (a = 0.05) using the 5-step hypothesis testing procedure (show ALL steps). Make sure to clearly state the null and alternative hypotheses in formal notation. Round all values to 2 decimal places. Show your work. Take a picture of…arrow_forward
- The concentration of cholesterol (a type of fat) in the blood is associated with the risk of developing heart disease, such that higher concentrations of cholesterol indicate a higher level of risk, and lower concentrations indicate a lower level of risk. If you lower the concentration of cholesterol in the blood, your risk of developing heart disease can be reduced. Being overweight and/or physically inactive increases the concentration of cholesterol in your blood. Both exercise and weight loss can reduce cholesterol concentration. However, it is not known whether exercise or weight loss is best for lowering cholesterol concentration. Therefore, a researcher decided to investigate whether an exercise or weight loss intervention is more effective in lowering cholesterol levels. To this end, the researcher recruited a random sample of inactive males that were classified as overweight. This sample was then randomly split into two groups: Group 1 underwent a calorie-controlled diet and…arrow_forwardIndicate whether the following are true or false. Explain why true or false. a. A standard linear model which is supposed to measure a causal relationship is called a structural equationarrow_forwardA highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data were collected during rush hour for six highways leading out of the city. Traffic Flow(y) Vehicle Speed(x) 1,258 35 1,329 40 1,227 30 1,336 45 1,348 50 1,125 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2.(Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) ŷ = ?? (b) Use ? = 0.01 to test for a significant relationship. State the null and alternative hypotheses. -H0: One or more of the parameters is not equal to zero.Ha: b0 = b1 = b2 = 0 -H0: b0 = b1 = b2 = 0Ha: One or more…arrow_forward
- Intensive care units (ICUS) generally treat the sickest patients in a hospital. ICUS are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUS as efficiently as possible in hospital. According to a 2017 large-scale study of elderly ICU patients, the average length of stay in the ICU is 3.4 days (Critical Care Medicine journal article). Assume that this length of stay in the ICU has an exponential distribution. Do not round intermediate calculations. a. What is the probability that the length of stay in the ICU is one day or less (to 4 decimals)? b. What is the probability that the length of stay in the ICU is between two and three days (to 4 decimals)? c. What is the probability that the length of stay in the ICU is more than five days (to 4 decimals)?arrow_forwardMaintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in following table ("Maintaining balance while," 2013). Table: Forward/backward Sway (in mm) of Elderly Subjects 19 30 20 19 29 25 21 24 50 Do the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Test at the 5% level. (vii) Calculate and enter test statistic Enter value in decimal form rounded to nearest ten-thousandth, with appropriate sign (no spaces). Examples of correctly entered answers: –2.0140 –0.0307 +0.6000 +1.0009 (viii) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic. Enter value in decimal form rounded…arrow_forwardMaintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in following table ("Maintaining balance while," 2013). Table: Forward/backward Sway (in mm) of Elderly Subjects 19 30 20 19 29 25 21 24 50 Do the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Test at the 5% level. (iv) Determine sample mean x :iv Determine sample mean x : Enter answer to nearest ten-thousandth, without units of measure. Examples of correctly entered answers: 11.2385 0.0079 3.0500 7.4000 (v) Determine sample standard deviation s :v Determine sample standard deviation s : Enter in decimal form to nearest thousandth. Do not enter units of measure. Examples…arrow_forward
- In a study on speed control, it was found that the main reasons for regulations were to make traffic flow more efficient and to minimize the risk of danger. An area that was focused on in the study was the distance required to completely stop a vehicle at various speeds . Use the following table to answer the questions. MPH Braking Distance 20 20 30 45 40 81 50 133 60 205 80 411 Assume MPH is going to be used to predict stopping distance. Which of the two variables in the independent variable? Which is the dependent variable? What type of variable is the dependent variable What type of variable is the independent variable? Construct a scatter plot IS there a relationship between the two variables? a) Positive b) Negativearrow_forwardA highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data were collected during rush hour for six highways leading out of the city. Traffic Flow(y) Vehicle Speed(x) 1,254 35 1,330 40 1,228 30 1,334 45 1,351 50 1,126 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) ŷ = (b) Use ? = 0.01 to test for a significant relationship. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = (c)…arrow_forwardA highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data were collected during rush hour for six highways leading out of the city. Traffic Flow(y) Vehicle Speed(x) 1,254 35 1,330 40 1,228 30 1,334 45 1,351 50 1,126 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) ŷ = (b) Use ? = 0.01 to test for a significant relationship. State the null and alternative hypotheses. H0: b0 = b1 = b2 = 0Ha: One or more of the parameters is not equal to zero.H0: One or more of the parameters is…arrow_forward