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Student GPAs Consider the set of all students enrolled in your statistics course this term. Suppose you're interested in learning about the current grade point averages (GPAs) of this group. 3. Define the population and variable of interest. b. Is the variable qualitative or quantitative? c. Suppose you determine the GPA of every member of the class. Would this determination represent a census or a sample? d. Suppose you determine the GPA of 10 members of the class. Would this determination represent a census or a sample? e. If you determine the GPA of every member of the class and then calculate the average, how much reliability does your calculation have as an "estimate" of the class average GPA? f. If you determine the GPA of 10 members of the class and then calculate the average, will the number you get necessarily be the same as the average GPA for the whole class? On what factors would you expect the reliability of the estimate to depend? g. What must be true in order for the sample of 10 students you select from your class to be considered a random sample?Medicinal value of plants. Sea buckthorn (Hippophae), a plant that typically grows at high altitudes in Europe and Asia, has been found to have medicinal value. The medicinal properties of berries collected from sea buckthorn were investigated in Academia Journal of Medicinal Plants (Aug. 2013). The following variables were measured for each plant sampled. Identify each as producing quantitative or qualitative data. a. Species of sea buckthom (H. rhamnoides, H. gyantsensis, H. neurocarpa, H. tibetana, or H. salicifolia) b. Altitude of collection location (meters) c. Total flavonoid content in berries (milligrams per gram)Complete the following table: Grade on Statistics Exam | Frequency | Relative Frequency A: 90-100 108 B: 80-89 36 C: 85-79 90 D: 50-84 30 F: Below 50 28 Total 200 1.00A qualitative variable with three classes (X, Y, and Z) is measured for each of 20 units randomly sampled from a target population. The data (observed class for each unit) are as follows: X XZXY Y Y X X Z X Y Y X Y YX a. Compute the frequency for each of the three classes. b. Compute the relative frequency for each of the three classes. c. Display the results from part a in a frequency bar graph. d. Display the results from part b in a pie chart.Do social robots walk or roll? According to the United Nations, social robots now outnumber industrial robots worldwide. A social (or service) robot is designed to entertain, educate, and care for human users. In a paper published by the International Conference on Social Robotics (Vol. 8414, 2010). design engineers investigated the trend in the design of social robots. Using a random sample of 106 social robots obtained through a Web search, the engineers found that 63 were built with legs only. 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. This information is portrayed in the accompanying graphic. 3. What type of graph is used to describe the data? b. Identify the variable measured for each of the 108 robot designs. c. Use the graph to identify the social robot design that is currently used the most. d. Compute class relative frequencies for the different categories shown in the graph. e. Use the results from part d to construct a Pareto diagram for the data. 70 40 Both Love Only Wheel Only Type of Helvetic LinksPaying for music downloads. If you use the Internet, have you ever paid to access or download music? This was one of the questions of interest in a recent Pew Internet & American Life Project Survey (October 2010). Telephone interviews were conducted on a representative sample of 1,003 adults living in the United States. For this sample, 248 adults stated that they do not use the Internet, 249 revealed that they use the Internet but have never paid to download music, and the remainder (506 adults) stated that they use the Internet and have paid to download music. The results are summarized in the MINITAB pie chart shown. a. According to the pie chart, what proportion of the sample use the Internet and pay to download music? Verify the accuracy of this proportion using the survey results. b. Now consider only the 755 adults in the sample that use the Internet. Create a graph that compares the proportion of these adults that pay to download music with the proportion that do not pay- Ple Chart of Download-Music Na Internet In barrel . No Pay internet - PaidThe butterfly symbolizes the notion of personal change. Increasingly, people are turning to butterflies to consecrate meaningful events, such as birthdays, weddings, and funerals. To fill this need, a new industry has hatched. Due to the possibility of introducing an invasive species, butterfly suppliers are monitored by governmental agencies. Along with following regulations, butterfly suppliers must ensure quality and quantity of their product while maintaining a profit. To this end, an individual supplier may hire independent contractors to hatch the varieties needed. These entrepreneurs are paid a small fee for each chrysalis delivered, with a 50% bonus added for each hatched healthy butterfly. This fee structure provides little room for profit. Therefore, it is important that these contractors deliver a high proportion of healthy butterflies that emerge at a fairly predictable rate. In Florida, one such entrepreneur specializes in harvesting the black swallowtail butterfly. In nature, the female butterfly seeks plants, such as carrot and parsley, to harvest and lay eggs on. A newly hatched caterpillar consumes the host plant, then secures itself and sheds its skin, revealing a chrysalis. During this resting phase. environmental factors such as temperature and humidity may affect the transformation process. Typically, the black swallowtail takes about 1 week to complete its metamorphosis and emerge from its chrysalis. The transformation occasionally results in deformities ranging from wings that will not fully open to missing limbs. The Florida contractor believes that there are differences in quality and emergence time among his broods. Not having taken a scientific approach to the problem, he relies on his memory of seasons past. It seems to him that late-season butterflies emerge sooner and with a greater number of deformities than their earlyseason counterparts. He also speculates that the type and nutritional value of the food consumed by the caterpillar might contribute to any observed differences. This year he is committed to a more formal approach to his butterfly harvest. Since it takes 2 days to deliver the chrysalises from the contractor to the supplier, it is important that the butterflies do not emerge prematurely. It is equally important that the number of defective butterflies be minimized. With these two goals in mind, the contractor seeks the best combination of food source, fertilizer, and brood season to maximize his profits. To examine the effects of these variables on emergence time and number of deformed butterflies, the entrepreneur designed the following experiment. Eight identical pots were filled with equal amounts of a soil and watered carefully to ensure consistency. Two pots of carrot plants and two of parsley were set outside during the early part of the brood season. For the carrot pair, one pot was fed a fixed amount of liquid fertilizer, while the other was fed a nutritionally similar amount of solid fertilizer. The two pots of parsley were similarly fertilized. All four pots were placed next to each other to ensure similar exposures to environmental conditions such as temperature and solar radiation. Five black swallowtail caterpillars of similar age were placed into each container, each allowed to mature and form a chrysalis. The time from chrysalis formation until emergence was reported to the nearest day, along with any defects. The same procedure was followed with the four pots that were placed outdoors during the late brood season. Write a report describing the experimental goals and design for the entrepreneur's experiment. Follow the procedure outlined in the box on steps in designing and conducting an experiment (p. 44). Step 5(b). of this procedure is provided in the following table and should be included in your report. Florida Black Swallowtail Chrysalis Experiment Data Number Emergence Season Food Fertilizer Deformed Time (Days) Early Parsley P!IPS D 6,6.727 Early Parsley Liquid D 6, 7, 78.8 Early Carrot Solid 1 3,6,6, 78 Early Carrot Liquid 6,6, 78,8 Late Parsley Solic 2 2,3,4,4,5 Late Parsley Liquid 1 2, 3,4,5,5 Late Carrot Solid 2 3,3,3,4,5 Late Carrot Liquid 2,4,4.4,5 In your report, provide a general descriptive analysis of these data. Be sure to include recommendations for the combination of season, food source, and type of fertilizer that result in the fewest deformed butterflies while achieving a long emergence time. Conclude your report with recommendations for further experiments. For each proposed experiment, be sure to do the following: Define the factors that affect the response variables.Genealogy research. The Journal of Family History (Jan. 2010) investigated the genealogy of a certain Korean clan. Of interest was whether or not a family name continued into the next generation in the clan genealogy (called a continued line) or dropped out (called a dropout line). Side by- side pie charts were used to describe the rate at which certain occupational titles of clan individuals occurred within each line type. Similarly constructed MINITAB bar charts are shown on p. 39. a. Identify the two qualitative variables graphed in the side-by-side pie charts. b. Give a full interpretation of the charts. Identify the major differences (if any) between the two line groups. MINITAB Output for Exercise 2.14 CLAN TITLE\fCurbing street gang gun violence. Operation Ceasefire is a program implemented to reduce street gang gun violence in the city of Boston. The effectiveness of the program was examined in the Journal of Quantitative Criminology (Mar. 2014). Over a 5-year period (2008-2010), there were 80 shootings involving a particular Boston street gang (called the Lucerne Street Doggz). The information in the table breaks down these shootings by year and by who was shot (gang members or non-gang members). Note: The Ceasefire program was implemented at the end of 2007. Shootings of Shootings of Total Gang Non-Gang Year Shootings Members Members 2005 37 30 2007 30 22 2008 3 2009 4 2010 Totals 62 18 Source Briga, A A. Hercau, I M., and Papachraios, A. V. "Deterring gang- involved gun violence: Memuring the impact of Boston's Operation Ceasefire on sirect pang behavior." Journal of Vawantsnive Criminology, Val 31 Na 1, Mar. 2014 (adapted from Figure ]). a. Construct a Pareto diagram for the total annual shootings involving the Boston street gang. b. Construct a Pareto diagram for the annual shootings of the Boston street gang members. c. Based on the Pareto diagrams, comment on the effectiveness of Operation Ceasefire.The Random Numbers applet generates a list of n random numbers from 1 to N, where n is the size of the sample and N is the size of the population. The list generated often contains repetitions of one or more numbers. a. Using the applet Random Numbers, enter 1 for the minimum value, 10 for the maximum value, and 10 for the number of samples. Then click on Sample. Look at the results, and list any numbers that are repeated and the number of times each of these numbers occurs. b. Repeat part (a). changing the maximum value to 20 and keeping the size of the sample fixed at 10. If you still have repetitions, repeat the process, increasing the maximum value by 10 each time but keeping the size of the sample fixed. What is the smallest maximum value for which you had no repetitions? c. Describe the relationship between the population size (maximum value) and the number of repetitions in the list of random numbers as the population size increases and the sample size remains the same. What can you conclude about using a random number generator to choose a relatively small sample from a large population?STEM experiences for girls. The National Science Foundation (NSF) promotes girls' participation in informal science, technology, engineering. and mathematics (STEM) programs. What has been the impact of these informal STEM experiences? This was the question of interest in the published study Cascading Influences: Long-Term Impacts of Informal STEM Experiences for Girls (Mar. 2013). A sample of 159 young women who recently participated in a STEM program were recruited to complete an online survey. Of these, only 27% felt that participation in the STEM program increased their interest in science. a. Identify the population of interest to the researchers. b. Identify the sample. c. Use the information in the study to make an inference about the relevant population.Drafting NFL quarterbacks. The Journal of Productivity Analysis (Vol. 35, 2011) published a study of how successful National Football League (NFL) teams are in drafting productive quarterbacks. Data were collected for all 331 quarterbacks drafted over a 38-year period. Several variables were measured for each QB, including draft position (one of the top 10 players picked, selection between picks 11-50. or selected after pick 50), NFL winning ratio(percentage of games won), and QB production score (higher scores indicate more productive QBs). The researchers discovered that draft position was only weaklyrelated to a quarterback's performance in the NFL. They concluded that "quarterbacks taken higher [in the draft] do not appear to perform any better." a. What is the experimental unit for this study? b. Identify the type (quantitative or qualitative) of each variable measured. C. Is the study an application of descriptive or inferential statistics? Explain
