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The 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 Solid 6,6.727 Early Parsley Liquid 6. 7 78.8 Early Carrot Solid 1 3, 6,6, 78 Early Carrot Liquid 6, 6, 78,8 Late Parsley Solid 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 0 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: State the problem to be solved and define the response variables.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)Use the applet entitled Mean versus Median to find the mean and median of each of the three data sets presented in Exercise 2 59. For each data set, set the lower limit to a number less than all of the data, set the upper limit to a number greater than all of the data, and then click on Update. Click on the approximate location of each data item on the number line. You can get rid of a point by dragging it to the trash can. To clear the graph between data sets, simply click on the trash can. 3. Compare the means and medians generated by the applet with those you calculated by hand in Exercise 2.59. If there are differences, explain why the applet might give values slightly different from the hand-calculated values. b. Despite providing only approximate values of the mean and median of a data set, describe some advantages of using the applet to find those values. (Reference Exercise 2.50) Calculate the mean, median, and mode for each of the following samples: a. 7, -2 3, 3, 0. 4 b. 2. 3, 5. 3, 2, 3. 4, 3, 5, 1, 2. 3, 4 C. 51, 50, 47. 50, 48. 41, 59, 68, 45, 37The 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.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?The Random Numbers applet can be used to select a random sample from a population, but can it be used to simulate data? In parts (a) and (b). you will use the applet to create data sets. Then you will explore whether those data sets are realistic. a. Consider the number of customers waiting in line to order at a fast-food outlet. Use the Random Numbers applet to simulate this data set by setting the minimum value equal to 0, the maximum value equal to 99, and the sample size equal to 30. Explain what the numbers in the list produced by the applet represent in the context of the problem. Do the numbers produced by the applet seem reasonable? Explain. b. Use the Random Numbers applet to simulate grades on a statistics test by setting the minimum value equal to 0, the maximum value equal to 100, and the sample size equal to 30. Explain what the numbers in the list produced by the applet represent in this context. Do the numbers produced by the applet seem reasonable? Explain. c. Referring to parts (a) and (b). why do the randomly generated data seem more reasonable in one situation than in the other? Comment on the usefulness of using a random-number generator to produce data.Suppose you're given a data set that classifies each sample unit into one of four categories: A, B. C. or D. You plan to create a computer database consisting of these data, and you decide to code the data as A = 1, B = 2. 0 = 3, and D = 4. Are the data consisting of the classifications A, B. C. and D qualitative or quantitative? After the data are input as 1, 2. 3, or 4, are they qualitative or quantitative? Explain your answers.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.Sprint speed training. The Sport Joumal (Winter 2004) reported on a study of a speed-training program for high school football players. Each participant was timed in a 40-yard sprint both before and after training. The researchers measured two variables: (1) the difference between the before and after sprint times (in seconds), and (2) the category of improvement ("improved." "no change." and "worse") for each player. a. Identify the type (quantitative or qualitative) of each variable measured. b. A total of 14 high school football players participated in the speed-training program. Does the data set collected represent a population or a sample? Explain.Corrosion prevention of buried steel structures. Engineers have designed tests on underground steel structures that measure the potential for corrosion. In Materials Performance (Mar. 2013). two tests for steel corrosion- called "instant-off" and "instant-on" potential-were compared. The tests were applied to buried piping at a petrochemical plant. Both the "instant-off and "instant- on corrosion measurements were made at each of 19 different randomly selected pipe locations. One objective of the study is to determine if one test is more desirable (i.e., can more accurately predict the potential for corrosion) than the other when applied to buried steel piping. a. What are the experimental units for this study? b. Describe the sample. c. Describe the population. d. Is this an example of descriptive or inferential statistics
