must answer all questions in file and question with a computer symbol must be done with the use of python or google collab (both platforms are acceptable)
DS 1000 Assignment 3 – due July 28, 2022, at 23:55 EST Chapters 8, 9, 13, 15, 16 and 32 • Questions with the computer symbol must be answered using Python. All codes must be provided in the PDF of your answers. • Submissions must be done via Gradescope. Please see instructions on OWL. Question 1 (10 pts) A utility company was interested in knowing if agricultural customers would use less electricity during peak hours if their rates were different during those hours. (Agricultural energy use is substantial, for things like irrigation, lighting, wind turbines to reduce frost damage, and so on.) Customers who volunteered for the study were randomly assigned to continue to get standard rates or to receive the time-of-day rate structure. Special meters were attached that recorded usage during peak and off-peak hours, which the customers could read. The technician who read the meter did not know what rate structure each customer had. a) (2 pts) What was the explanatory variable in this experiment? b) (2 pts) What was the response variable in this experiment? c) (3 pts) Was this experiment single-blind, double-blind, or neither? Explain. d) (3 pts) Did this experiment use matched pairs, blocks, or neither? Explain. Question 2 (4 pts) The 1990s and early 2000s could be considered the steroids era in Major League Baseball, as many players have admitted to using the drug to increase performance on the field. If a sports writer wanted to compare home run totals from the steroids era to an earlier decade, say the 1960s, explain why this would be an observational study. Could the writer conclude that it was the steroids that caused the increase in home runs? Why or why not? Question 3 (12 pts) A manufacturing company employs 21 project managers, 63 foremen and 336 labourers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month. a) (3 pts) Suppose the company is considering using a simple random sample of employees each month. Why do you think this sampling strategy might not provide the representative sample that the company seeks. b) (2 pts) Do you see any other danger of bias in the company’s plan to interview employees? Explain. c) (3 pts) Propose a better sampling strategy for the company to use. Explain why it is better. d) (4 pts) Using Python code, generate a random sample of 20 employees using the sampling strategy you described in part c). Be sure to explain how you assigned labels to any groups that might be in your sampling strategy. Question 4 (12 pts) Some people claim they can get relief from migraine headache pain by drinking a large glass of ice water. Researchers plan to enlist several people who suffer from migraines in a test. When a participant experiences a migraine headache, he or she will take a pill that may be a standard pain reliever or a placebo. Half of each group will also drink ice water. Participants will then report the level of pain relief they experience. a) (2 pts) Identify the factors in the experiment and the number of levels of each. How many treatments are there? b) (3 pts) Use a diagram like Figure 9,2 (page 228 of the textbook) to display the treatments in the experiment. Then outline the design of a completely randomized experiment to compare these treatments. c) (3 pts) Suppose there are 40 subjects available for the experiment and they are randomly assigned to the treatments with an equal number of subjects in each treatment. Explain how you would number subjects and then randomly assign the subjects to the treatments. d) (4 pts) Use Python code to generate the sample you have described in part c). Question 5 (10 pts) In its monthly report, a local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and six of the cats are male. a) (3 pts) Find the probability if an animal is selected at random that the pet is male, given that it is a cat. b) (3 pts) Find the probability if an animal is selected at random that the pet is a cat, given that it is female. c) (4 pts) Are the species and sex of the animals independent? Explain. Question 6 (12 pts) The three major options on a car model are an automatic transmission (A), a sunroof (B), and an upgraded stereo (C). The probabilities that a customer requests these options are as follows: P(A) = 0.70 P(B) = 0.80 P(C) = 0.75 P(A and B) = 0.65 P(A and C) = 0.55 P(B and C) = 0.60 P(A and B and C) = 0.53 Compute the probabilities of the following events. a) (4 pts) Make a Venn diagram of the events A, B, and C. As in Figure 13.4 (page 297 of the textbook), mark the probabilities of every intersection involving these events. Use this diagram for parts b) through d). b) (2 pts) What is the probability that the next customer will select none of the three options? Show all your work. c) (2 pts) What is the probability that the next customer will request only an automatic transmission and neither of the other two options? Show all your work. d) (2 pts) If a customer requests a sunroof, what is the probability that he or she will request an upgraded stereo? e) (2 pts) If a customer does not request a sunroof, what is the probability that he or she will request an upgraded stereo? Question 7 (10 pts) According to Canadian Radio-television and Telecommunications Commission, the average number of hours of TV viewing among adults is 27 hours per week. Suppose the standard deviation is 6.7 hours and a random sample of 42 Canadian households is taken. a) (3 pts) Let �̅� be the average number of hours of TV viewing among adults in the sample. What is the approximate distribution of �̅� according to the Central Limit Theorem? b) (3 pts) What is the probability that the sample average is more than 30.5 hours? c) (4 pts) If the sample average actually is more than 30.5 hours, what would it mean in this context? Question 8 (12 pts) A community health association is interested in estimating the average number of maternity days women stay in the local hospital. A random sample is taken of 36 women who gave birth in the hospital during the past year (dataset maternity-days.csv). The following numbers of maternity days each woman was in the hospital are rounded to the nearest day. 3 3 4 3 2 5 3 1 4 4 2 3 5 3 2 4 3 2 1 6 3 4 3 3 5 2 3 3 5 4 3 5 4 3 4 2 a) (4 pts) Make a histogram of the data to verify that the data follow a Normal distribution quite closely. b) (4 pts) Use the data and a population standard deviation of 1.17 to construct a 98% confidence interval to estimate the average maternity stay in the hospital for all women who give birth in this hospital. Show your work. c) (4 pts) Would it be correct to say that the probability is 98% that the mean number of maternity days for the population lies in the interval you computed in part b)? Explain your answer. Question 9 (18 pts) In a survey, students gave their study time per week (in hours). The 22 values (dataset study- time.csv) are shown below: 15.0 10.0 10.0 15.0 25.0 7.0 3.0 8.0 10.0 11.0 7.0 5.0 15.0 7.5 7.5 12.0 10.5 6.0 10.0 7.5 10.0 7.0 We would like to obtain a 95% confidence interval for the population mean and the population median of the study hours data. a) (5 pts) Make a histogram of the data to verify that the data does not follow a Normal distribution. b) (3 pts) Can the Central Limit Theorem be used here to create a confidence interval for the mean? Explain. c) (5 pts) Construct a percentile-based 95% bootstrap confidence interval for the mean number of study hours per week for the students. Use 1000 bootstrap samples. d) (5 pts) Construct a percentile-based 95% bootstrap confidence interval for the median number of study hours per week for the students. Use 1000 bootstrap samples.