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NCSU MAE 206 - HW 1

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HW1HW5 - CopyHW 1 Suggested Practice Homework: if you want more practice before homework or exams 1. Explain the differences between a completely randomized design, randomized block de- sign, and matched pairs design. Create an original example of each.2. Explain the differences and benefits of simple random sampling, systematic sampling,cluster sampling, and stratified sampling.Homework: Collected and Graded 1. A poll is planned to determine what proportion of all students favor an increase in feesto support a new track and field stadium. For each study design, identify the issue (ifany exists) that best characterizes the problem with the study. Some answers may beused more than once.(a) The very popular head coach of the track team will personally survey randomlysampled students about their opinions of the facility.A. UndercoverageB. Voluntary response sampleC. Response biasD. Nonresponse biasE. No issue(b) Questionnaires will be left on tables by the student union. When 1000 question- naires are completed, the results will be reported.A. UndercoverageB. Voluntary response sampleC. Response biasD. Nonresponse biasE. No issue(c) A random sample of 1000 students will be drawn from the list of all students signedup to the athletics newsletter.A. UndercoverageB. Voluntary response sampleC. Response biasD. Nonresponse biasE. No issue(d) A random sample of 2000 students is selected, but only 1000 students respondbecause a large number of students have been flagging athletics department emailsas spam because of the volume of emails that they send.A. UndercoverageB. Voluntary response sampleC. Response biasD. Nonresponse biasE. No issue2. A study was done to determine if the size of tubing (small or large) and temperature(200F, 250F, 300F) of an oven affects the durability (measured in hours) of a certaintype of plastic tubing. 36 pieces of tube (each can be cut to small or large size) areavailable to be used.(a) Define the population and sample.(b) Is this an observational study or an experiment? Explain.(c) Describe precisely how you would conduct a completely randomized design in thissetting.(d) Explain why randomization is important in the above experiment.3. Researchers want to know how various diets affect the weight (in grams) of baby chickens.They have two species of chicks (Rhode Island Reds & Leghorns) and 4 diets types (A,B, C, & D). There were a total of 48 chicks in the study, which are weighed at 3 weeks.(a) Identify the factors, treatments, & response variables.(b) How many replicates are in this study?(c) Why is replication important in a study?(d) Explain the design of this study. Does it use blocking? If so, how?(e) Explain the 2 main sources of variability in the response variable.2(f) List 4 sources of experimental error and speculate on how those errors could existin this study.4. An experiment was conducted to determine if factor A, time frozen (30 min or 60 min), and/or factor B, topping (cheese only or cheese with green pepper), had an effect on thequality (measured on a scale of 0 100, integers only) of a brand of pizza. The pizzaswere selected for the study by creating a list of all available pizzas from the companyand using a random number generator to select random pizzas. The data are given below:Pizza Quality Rating Time Topping1 77 30 Cheese2 70 30 Cheese3 85 30 Cheese with green pepper4 89 30 Cheese with green pepper5 62 60 Cheese6 65 60 Cheese7 75 60 Cheese with green pepper8 77 60 Cheese with green pepper(a) What type of sampling was used in this study?(b) Which explanatory variables are factors? Which are covariates?(c) Give an example of a variable we might control for and state why we would wantto control for it in the above

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