Stat 31] Homework 1 l. The following table summarizes data from the I SR Launch Vehicle Database, 2019 Feb 10 Edition, and shows the number of space launches in the US by the type of launching agency and the outcome of the launch (suowss of failure). I957 - 1999 2000 - 2018 Failure Success Failure Success a) Whatvuiablesweseeoemdoneachlaunohmcmtedsemmmuytableshownabove? b) State whether each variable is numerical or categorical. If numerical. state whether it is continuous or discrete. If categorical. state whether it is ordinal or not. c) Suppose we wanted to study how the success rate of launches vary between launching agencies and over time. In this analysis, which variable would be the response variable and which variable would be the explanatory variable? In a study of three nationally representative large-scale datasets from Ireland, the United States, and the United Kingdom (n = 17,247), teenagers between the ages of 12 to l5 were asked to keep a diary of their screen time and answer questions about how they felt or acted. The answers to these questions were then used to compute a psychological well-being score. Additional data were collected and included in the analysis, such as each child's sex and age, and on the mother's education, ethnicity, psychological distress, and employment. The study concluded that there is little clear-cut evidence that screen time decreases adolescent well-being (Orben and Bankney-Przybylski, 2018). a) What type of study is this? Briey explain. b) Identify the explanatory variables. c) Identify the response variable. d) Comment on whether the results of the study can be generalized to the population, and why. e) Comment on whether the results of the study can be used to establish causal relationships. A city council has requested a household survey be conducted in a suburban area of their city. The area is broken into many distinct and unique neighborhoods, some including large homes, some with only apartments, and others a diverse mixture of housing structures. For each part below, identify the sampling methods described, and describe the statistical pros and cons of the method in the city's context. a) Randomly sample 200 households from the city. b) Divide the city into 20 neighborhoods, and sample 10 households from each neighborhood. c) Divide the city into 20 neighborhoods, randomly sample 3 neighborhoods. and then sample all households from those 3 neighborhoods. d) Divide the city into 20 neighborhoods, randomly sample 8 neighborhoods, and then randomly sample 50 households from those neighborhoods. e) Sample the 200 households closest to the city council ofces. Stat 311 Homework 1 4. Researchers studying the relationship between honesty, age and self-control conducted an experiment on 160 children between the ages of 5 and 15. The researchers asked each child to toss a fair coin in private and to record the outcome (white or black) on a paper sheet, and said they would only reward children who report white. Half the students were explicitly told not to cheat and the others were not given any explicit instructions. Differences were observed in the cheating rates in the instruction and no instruction groups, as well as some differences across children's characteristics within each group (Bucciol and Piovesan, 2011). a) Identify the population of interest and the sample in this study. b) Comment on whether the results of the study can be generalized to the population, and if the findings of the study can be used to establish causal relationships. 5. Suppose you want to estimate the percentage of videos on YouTube that are cat videos. It is impossible for you to watch all videos on YouTube so you use a random video picker to select 1000 videos for you. You find that 2% of these videos are cat videos. Determine which of the following is an observation, a variable, a sample statistic (value calculated based on the observed sample), or a population parameter. a) Percentage of all videos on YouTube that are cat videos. b) 2%. c) A video in your sample. d) Whether a video is a cat video. 6. Using R as a calculator a) Use the $ notation shown in the video to write out the equations for the circumference and area of a circle. Remember that C = 2xr and A = mr. To get Greek letters to show in an equation, use \\pi for example. To get a multiplication sign in the formula use \\ times. b) Write code to calculate the circumferences and areas of circles with radii of 0.5 and 2 cm. If you want, you can create a variable such as rad