Probability and Statistics:-
On-Time Flights The following data represent the arrival status of Southwest Flight 0426 from Dallas' Love Field to San Antonio International Airport for 14 consecutive flights. Source: U.S. Department of Transportation L O O L LL O O L O O O OL Status is indicated as on time (0) or late (L). A late arrival is defined as a gate arrival that is more than 10 minutes after the scheduled arrival. What can you conclude about the randomness of the arrival status at the a=0.05 level of significance?On-Time Flights The following data represent the arrival status of American Airlines Flight 0715 from Washington DC's Ronald Reagan Airport to Chicago's O'Hare International Airport for 15 consecutive flights. Source: U.S. Department of Transportation LOO 0 0 0 0 LLL O L0 0 0 Status is indicated as on time (O) or late (L). A late arrival is defined as a gate arrival that is more than 10 minutes after the scheduled arrival. What can you conclude about the randomness of the arrival status at the 0=0.05 level of significance?Quality ControlThe quality-control manager of a bottling company wants to discover whether a filling machine overor underfills 16-ounce bottles randomly. The following data represent the filling status of 20 consecutive bottles: AAAAAAAR R R RAAAAAAAR R A bottle is rejected (R) if it is either overfilled or underfilled. A bottle is accepted (A) if it is filled according to specification. Test the randomness of the filling machine in the way that it over- or underfills at the 0=0.05 level of significance.Quality ControlThe quality-control manager of a candy company wants to discover whether a filling machine over- or underfills 16-ounce bags randomly. The following data represent the filling status of 18 consecutive bags: AAAAAR R RAAAAAAAAAAA bag is rejected (R) if it is either overfilled or underfilled. A bag is accepted (A) if it is filled according to specification. Test the randomness of the filling machine in the way that it over- and underfills at the a=0.05 level of significance.Housing Prices on ZillowThe Web site zillow.com allows us to research real estate listings. One neat feature of the site is the "Zestimate," which represents the price Zillow believes the property should sell for. If the Zestimate is accurate, the median difference between the actual selling price and the Zestimate should be zero. The following data represent the difference between the actual selling price and Zestimate for a random sample of 10 real estate transactions. Do the data suggest the Zestimate is inaccurate? Use the o = 0.05 level of significance. Note:A normal probability plot indicates the data are not normal. Source zillow.com 2500 -500 -79.500 -13.500 -500 -1000 14.500 3.500 -12 500 -6000The 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 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 6.6.717 Early Parsley Liquid 6. ZZ8.8 Early Carrot Sali 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 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.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 0 6. 7 78.8 Early Carrot Solid 3,6,6, 78 Early Carrol Liquid 0 6, 6, 78,8 Late Parsley Solid 2 2, 3,4,4,5 Late Parsley Liquid 2, 3,4,5,5 Late Carrot Solid 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: Define the factors that affect the response variables.In Problems determine if the variable is qualitative or quantitative. If the variable is quantitative, determine if it is discrete or continuous. State the level of measurement of the variable Time to complete the 500-meter race in speed skating.Births by Season An obstetrician wants to determine if the distribution of births is the same for the periods January to March April to June, July to September, and October to December. She randomly selected 10 days within each time frame and obtained the results shown in the following table: Source: National Center for Health Statistics. January-March April-June July-September| October-December 10.456 10,799 11,485 11,281 11,574 11,743 12,475 11,406 12 321 11,857 12,454 11,827 11,651 11,808 12,193 8.708 8,521 10,982 11.244 12,022 11,621 9.184 12,081 11,930 11,321 12,357 11,387 11.054 7,706 12,251 9.055 11,431 10.872 11,918 12,319 12,818 10.837 11,212 12.927 10,824 (a) State the null and alternative hypotheses. (b)The sums of the ranks in each category are as follows: January-March April-June | July-September | October-December Sample size 10 10 10 10 Sum of ranks 149 207 287 197 Use this information to compute the test statistic. (c) What is the critical value at the a = 0.05 level of significance? (d) State your conclusion. (e) Draw side-by-side boxplots to support your conclusion.Shapely Glasses Does the shape of a glass play a role in determining the amount of time it takes to finish the drink? Researchers identified 150 male and female self-professed social drinkers. One week the subjects were given a 12 ounce beer with either a straight glass or a curved glass. A week later the subjects were given a 12 ounce beer in the other glass. The first week, subjects were given a glass and asked to consume the drink at their own pace while watching television. The time to complete the drink was measured. During the second week, the subjects were given the other shaped glass and asked to complete a computer task. Again, the time to complete the drink was measured. The type of glass given in the first week was determined randomly. The researchers found that the time to complete the drink was significantly faster for the curved glass. Source: A. S. Attwood, N. E. Scott-Samuel, G. Stothart, M. R. Munafo (2012) "Glass Shape Influences Consumption Rate for Alcoholic Beverages." PLOS ONE 7(8): e43007. doi: 10. 1371/journal. pone.0043007. (a) What type of experimental design is this? (b) Who are the subjects? (c) What is the treatment? (d) What is the response variable? Is it qualitative or quantitative? (e) Explain the role randomization plays in this experiment. (f) Draw a figure that illustrates the design.Read the following description of an observational study and determine whether it is a cross- sectional, a case-control, or a cohort study. Explain your choice. The Cancer Prevention Study II (CPS-II) examines the relationship among environmental and lifestyle factors of cancer cases by tracking approximately 1.2 million men and women. Study participants completed an initial study questionnaire in 1982 providing information on a range of lifestyle factors, such as diet, alcohol and tobacco use, occupation, medical history, and family cancer history. These data have been examined extensively in relation to cancer mortality. The vital status of study participants is updated biennially. Source: American Cancer SocietyRead the following description of an observational study and determine whether it is a cross- sectional, a case-control, or a cohort study. Explain your choice. The Cancer Prevention Study II (CPS-II) examines the relationship among environmental and lifestyle factors of cancer cases by tracking approximately 1.2 million men and women. Study participants completed an initial study questionnaire in 1982 providing information on a range of lifestyle factors, such as diet, alcohol and tobacco use, occupation, medical history, and family cancer history. These data have been examined extensively in relation to cancer mortality. The vital status of study participants is updated biennially. Source: American Cancer SocietyObtaining a Simple Random Sample The mayor of a small town wants to conduct personal interviews with small business owners to determine if there is anything the mayor could do to help improve business conditions. The following list gives the names of the companies in the town. Obtain a simple random sample of size 5 from the companies in the town. Allied Tube and Conduit Lighthouse Financial Senese's Winery Bechstien Construction Co. | Mill Creek Animal Clinic Skyline Laboratory Cizer Trucking Co. Nancy's Flowers Solus, Maria, DDS D&M Welding Norm's Jewelry Trust Lock and Key Grace Cleaning Service Papoose Children's Center | Ultimate Carpet Jiffy Lube Plaza Inn Motel Waterfront Tavern Levin, Thomas, MD Risky Business Security WPA PharmacyCorn Production The following data represent the number of corn plants in randomly sampled rows (a 17-foot by 5-inch strip) for various types of plot. Source: Andrew Dieter and Brad Schmidgall, Joliet Junior College Plot Type Number of Plants Sludge plot 25 27 33 30 28 27 Spring disk 32 30 33 35 34 34 No til Spring Chisel 30 2 Do the data indicate that the distribution for each type of plot is the same at the o = 0.05 level of significance?Soybean Yield The following data represent the number of pods on a random sample of soybean plants for various types of plot Source: Andrew Dieter and Brad Schmidgall, Joliet Junior College Plot Type Pods Liberty Fall plowed No till Chisel plowed Round-up ready Do the data indicate that the distribution for each type of plot is the same at the o = 0.05 level of significance?In Problem, a research objective is presented. For each, identify the population and sample in the study. Folate and Hypertension Researcher John P. Forman and co-workers want to determine whether or not higher folate intake is associated with a lower risk of hypertension (high blood pressure) in younger women (27 to 44 years of age). To make this determination, they look at 7373 cases of hypertension in younger women and find that younger women who consume at least 1000 micrograms per day (up/d)) of total folate (dietary plus supplemental) had a decreased risk of hypertension compared with those who consume less than 200 mg/d. Source: John P. Forman, MD; Eric B. Rimm. ScD; Meir J. Stampfer, MD; Gary C. Curhan, MD. ScD, "Folate Intake and the Risk of Incident Hypertension among US Women." Journal of the American Medical Association 203:320-320, 2005Reaction Time In an online psychology experiment sponsored by the University of Mississippi, researchers asked study participants to respond to various stimuli. Participants were randomly assigned to one of three groups. Subjects in the simple group were required to respond as quickly as possible after a stimulus was presented. Subjects in the goo-go group were required to respond to a particular stimulus while disregarding other stimuli. Finally, subjects in the choice group needed to respond differently to different stimuli. Depending on the type of whistle sound, the subject had to press a certain button. The reaction time (in seconds) for each stimulus is presented in the following table: Source: Psych Experiments; University of Mississippi, www.olemiss.edu/psychexps/. Simple | Go/No-Go | Choice 0.430 0.588 0.581 0.498 0.375 0.498 0.480 0.409 0.519 0.376 0.613 0.538 0.402 0.481 0.484 0.320 0.355 0.725 Is the distribution for each stimulus the same at the a = 0.01 level of significance
