Problem 4
Find data on the Internet (or elsewhere) for two or more groups. Make appropriate displays to compare the groups, and interpret what you find.
Problem 19
The Environmental Protection Agency provides fuel economy and pollution information on over 2000 car models. Here is a boxplot of Combined Fuel Economy (using an average of driving conditions) in miles per gallon by vehicle Type (car, van, or SUV). Summarize what you see about the fuel economies of the three vehicle types.
Problem 23
A survey of major universities asked what percentage of incoming freshmen usually graduate "on time" in 4 years. Use the summary statistics given to answer the questions that follow. $$ \begin{array}{l|c} & \% \text { on Time } \\ \hline \text { Count } & 48 \\ \text { Mean } & 68.35 \\ \text { Median } & 69.90 \\ \text { StdDev } & 10.20 \\ \text { Min } & 43.20 \\ \text { Max } & 87.40 \\ \text { Range } & 44.20 \\ \text { 25th \%tile } & 59.15 \\ \text { 75th \%tile } & 74.75 \end{array} $$ a) Would you describe this distribution as symmetric or skewed? Explain. b) Are there any outliers? Explain. c) Create a boxplot of these data. d) Write a few sentences about the graduation rates.
Problem 25
A student study of the effects of caffeine asked volunteers to take a memory test 2 hours after drinking soda. Some drank caffeine-free cola, some drank regular cola (with caffeine), and others drank a mixture of the two (getting a half-dose of caffeine). Here are the 5-number summaries for each group's scores (number of items recalled correctly) on the memory test: $$ \begin{array}{l|c|c|c|c|c|c} & n & \text { Min } & \text { Q1 } & \text { Median } & \text { Q3 } & \text { Max } \\ \hline \text { No caffeine } & 15 & 16 & 20 & 21 & 24 & 26 \\ \text { Low caffeine } & 15 & 16 & 18 & 21 & 24 & 27 \\ \text { High caffeine } & 15 & 12 & 17 & 19 & 22 & 24 \end{array} $$ a) Describe the W's for these data. b) Name the variables and classify each as categorical or quantitative. c) Create parallel boxplots to display these results as best you can with this information. d) Write a few sentences comparing the performances of the three groups.
Problem 26
Here are the summary statistics for Verbal SAT scores for a high school graduating class: $$ \begin{array}{l|c|c|c|c|c|c|c|c} & n & \text { Mean } & \text { Median } & \text { SD } & \text { Min } & \text { Max } & \text { Q1 } & \text { Q3 } \\ \hline \text { Male } & 80 & 590 & 600 & 97.2 & 310 & 800 & 515 & 650 \\ \text { Female } & 82 & 602 & 625 & 102.0 & 360 & 770 & 530 & 680 \end{array} $$ a) Create parallel boxplots comparing the scores of boys and girls as best you can from the information given. b) Write a brief report on these results. Be sure to discuss the shape, center, and spread of the scores.
Problem 29
A class of fourth graders takes a diagnostic reading test, and the scores are reported by reading grade level. The 5-number summaries for the 14 boys and 11 girls are shown: $$ \begin{array}{llllll} \text { Boys: } & 2.0 & 3.9 & 4.3 & 4.9 & 6.0 \\ \text { Girls: } & 2.8 & 3.8 & 4.5 & 5.2 & 5.9 \end{array} $$ a) Which group had the highest score? b) Which group had the greater range? c) Which group had the greater interquartile range? d) Which group's scores appear to be more skewed? Explain. e) Which group generally did better on the test? Explain. f) If the mean reading level for boys was \(4.2\) and for girls was \(4.6\), what is the overall mean for the class?
Problem 30
In an experiment to determine whether seeding clouds with silver iodide increases rainfall, 52 clouds were randomly assigned to be seeded or not. The amount of rain they generated was then measured (in acre-feet). Here are the summary statistics: $$ \begin{array}{l|c|c|c|c|c|c|c} & n & \text { Mean } & \text { Median } & \text { SD } & \text { IQR } & \text { Q1 } & \text { Q3 } \\ \hline \text { Unseeded } & 26 & 164.59 & 44.20 & 278.43 & 138.60 & 24.40 & 163 \\ \text { Seeded } & 26 & 441.98 & 221.60 & 650.79 & 337.60 & 92.40 & 430 \end{array} $$ a) Which of the summary statistics are most appropriate for describing these distributions. Why? b) Do you see any evidence that seeding clouds may be effective? Explain.
Problem 31
Engineers at a computer production plant tested two methods for accuracy in drilling holes into a PC board. They tested how fast they could set the drilling machine by running 10 boards at each of two different speeds. To assess the results, they measured the distance (in inches) from the center of a target on the board to the center of the hole. The data and summary statistics are shown in the table: $$ \begin{array}{lc|l|l|l} & \text { Distance (in.) } & \text { Speed } & \text { Distance (in.) } & \text { Speed } \\ \hline & 0.000101 & \text { Fast } & & 0.000098 & \text { Slow } \\ & 0.000102 & \text { Fast } & & 0.000096 & \text { Slow } \\ & 0.000100 & \text { Fast } & & 0.000097 & \text { Slow } \\ & 0.000102 & \text { Fast } & & 0.000095 & \text { Slow } \\ & 0.000101 & \text { Fast } & & 0.000094 & \text { Slow } \\ & 0.000103 & \text { Fast } & & 0.000098 & \text { Slow } \\ & 0.000104 & \text { Fast } & & 0.000096 & \text { Slow } \\ & 0.000102 & \text { Fast } & & 0.975600 & \text { Slow } \\ & 0.000102 & \text { Fast } & & 0.000097 & \text { Slow } \\ & 0.000100 & \text { Fast } & & 0.000096 & \text { Slow } \\ \hline \text { Mean } & 0.000102 & & \text { Mean } & 0.097647 & \\ \text { StdDev } & 0.000001 & & \text { StdDev } & 0.308481 & \end{array} $$ Write a report summarizing the findings of the experiment. Include appropriate visual and verbal displays of the distributions, and make a recommendation to the engineers if they are most interested in the accuracy of the method.
Problem 32
A study examining the health risks of smoking measured the cholesterol levels of people who had smoked for at least 25 years and people of similar ages who had smoked for no more than 5 years and then stopped. Create appropriate graphical displays for both groups, and write a brief report comparing their cholesterol levels. Here are the data: $$ \begin{array}{llll|lll} {\text { Smokers }} &&&& {\text { Ex-Smokers }} \\ \hline 225 & 211 & 209 & 284 & 250 & 134 & 300 \\ 258 & 216 & 196 & 288 & 249 & 213 & 310 \\ 250 & 200 & 209 & 280 & 175 & 174 & 328 \\ 225 & 256 & 243 & 200 & 160 & 188 & 321 \\ 213 & 246 & 225 & 237 & 213 & 257 & 292 \\ 232 & 267 & 232 & 216 & 200 & 271 & 227 \\ 216 & 243 & 200 & 155 & 238 & 163 & 263 \\ 216 & 271 & 230 & 309 & 192 & 242 & 249 \\ 183 & 280 & 217 & 305 & 242 & 267 & 243 \\ 287 & 217 & 246 & 351 & 217 & 267 & 218 \\ 200 & 280 & 209 & & 217 & 183 & 228 \end{array} $$
Problem 33
A consumer organization compared gas mileage figures for several models of cars made in the United States with autos manufactured in other countries. The data are shown in the table: $$ \begin{array}{c|c|c|c} \begin{array}{c} \text { Gas Mileage } \\ (\mathrm{m} \mathrm{pg}) \end{array} & \text { Country } & \begin{array}{c} \text { Gas Mileage } \\ (\mathrm{mpg}) \end{array} & \text { Country } \\ \hline 16.9 & \text { U.S. } & 26.8 & \text { U.S. } \\ 15.5 & \text { U.S. } & 33.5 & \text { U.S. } \\ 19.2 & \text { U.S. } & 34.2 & \text { U.S. } \\ 18.5 & \text { U.S. } & 16.2 & \text { Other } \\ 30.0 & \text { U.S. } & 20.3 & \text { Other } \\ 30.9 & \text { U.S. } & 31.5 & \text { Other } \\ 20.6 & \text { U.S. } & 30.5 & \text { Other } \\ 20.8 & \text { U.S. } & 21.5 & \text { Other } \\ 18.6 & \text { U.S. } & 31.9 & \text { Other } \\ 18.1 & \text { U.S. } & 37.3 & \text { Other } \\ 17.0 & \text { U.S. } & 27.5 & \text { Other } \\ 17.6 & \text { U.S. } & 27.2 & \text { Other } \\ 16.5 & \text { U.S. } & 34.1 & \text { Other } \\ 18.2 & \text { U.S. } & 35.1 & \text { Other } \\ 26.5 & \text { U.S. } & 29.5 & \text { Other } \\ 21.9 & \text { U.S. } & 31.8 & \text { Other } \\ 27.4 & \text { U.S. } & 22.0 & \text { Other } \\ 28.4 & \text { U.S. } & 17.0 & \text { Other } \\ 28.8 & \text { U.S. } & 21.6 & \text { Other } \end{array} $$ a) Create graphical displays for these two groups. b) Write a few sentences comparing the distributions.
