BackEthics There are data showing that smoking is detrimental to good health. Given that people could be helped and lives could be saved by reducing smoking, is it ethical to graph the data in a way that is misleading by exaggerating the health risks of smoking?
Finding the Best Model
In Exercises 5–16, construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of the given data, and consider only linear, quadratic, logarithmic, exponential, and power models.
Dirt Cheap The Cherry Hill Construction company in Branford, CT sells screened topsoil by the “yard,” which is actually a cubic yard. Let the variable x be the length (yd) of each side of a cube of screened topsoil. The table below lists the values of x along with the corresponding cost (dollars).
Finding the Best Model
In Exercises 5–16, construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of the given data, and consider only linear, quadratic, logarithmic, exponential, and power models.
Sound Intensity The table lists intensities of sounds as multiples of a basic reference sound. A scale similar to the decibel scale is used to measure the sound intensity.
In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).
35 35 20 50 95 75 45 50 30 35 30 30
d. The accompanying normal quantile plot is obtained by using all 50 wait times at 10:00 AM for the Tower of Terror ride at Disney World. Based on this normal quantile plot, do the sample data appear to be from a normally distributed population?
In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).
35 35 20 50 95 75 45 50 30 35 30 30
b. Construct a boxplot.
Explore!
Exercises 11 and 12 provide two data sets from “Graphs in Statistical Analysis,” by F. J. Anscombe, the American Statistician, Vol. 27. For each exercise,
a. Construct a scatterplot.
Interpreting a Computer Display
In Exercises 9–12, refer to the display obtained by using the paired data consisting of weights (pounds) and highway fuel consumption amounts (mi/gal) of the large cars included in Data Set 35 “Car Data” in Appendix B. Along with the paired weights and fuel consumption amounts, StatCrunch was also given the value of 4000 pounds to be used for predicting highway fuel consumption.
Testing for Correlation Use the information provided in the display to determine the value of the linear correlation coefficient. Is there sufficient evidence to support a claim of a linear correlation between weights of large cars and the highway fuel consumption amounts?
Airport Data Speeds Listed below are the cellular data speeds (Mbps) from Sprint and Verizon measured at nine different airports (based on data from CNN). What would the presence of a correlation suggest about Sprint and Verizon?
Use Table 2-11 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation?
Using the data from Exercise 6 “Airport Data Speeds,” the linear correlation coefficient is r = 0.866
Tornado Alley A stemplot of the same data summarized in Exercise 1 is created, and one of the rows of that stemplot is 3 | 000144669. Identify the values represented by that row of the stemplot.
Computers As a quality control manager at Texas Instruments, you find that defective calculators have various causes, including worn machinery, human error, bad supplies, and packaging mistreatment. Which of the following graphs would be best for describing the causes of defects: histogram; scatterplot; Pareto chart; dotplot; pie chart?
In Exercises 9 and 10, construct the time-series graph.
Home Runs Listed below are the numbers of home runs in Major League Baseball for each year beginning with 1993 (listed in order by row). Is there a trend?
In Exercises 11 and 12 construct the Pareto chart.
Box Office Boffo Recent annual gross revenue (millions of dollars) for the leading movie studios are as follows: 20th Century Fox (1082), Buena Vista (3092), Paramount (757), Sony/Columbia (1304), Universal (1772), Warner Brothers (1941). Are these data likely to be reasonably accurate?
In Exercises 17–20, identify how the graph is deceptive.
Cost of Giving Birth According to the Agency for Healthcare Research and Quality Healthcare Cost and Utilization Project, the typical cost of a C-section baby delivery is $4500, and the typical cost of a vaginal delivery is $2600. See the following illustration.
V and Digital Ads Listed below are amounts (billions of dollars) spent on TV and digital advertising. The amounts are listed in order by year ending with the year 2022. The last few years are projected amounts (based on data from Magna Global). Construct a graph that reveals the story that the data are trying to tell. What story does the graph depict?
TV Ads:
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