| C:/Users/alexk/Downloads/ENVS278_F22_test1_STUDENT_v2.pdf v v Q2: Fast Fashion purchases [28 marks] A researcher wants to know what percentage of the student population at the University of Waterloo use online "fast fashion" retailers. They conducted an online survey of 214 students in one class (ENVS 278) in Fall 2022, and 124 students reported that they had used an online fast fashion retailer in the past 12 months. a. Sketch the sampling distribution for the proportion of fast fashion users at University of Waterloo (doesn't have to be to scale). Showing all necessary calculations, label the mean and standard deviation of the distribution on the x-axis. [6 marks] b. On the same sketch, label the upper and lower bound of a 95% confidence interval for the true population proportion. Show all necessary calculations. [5 marks] c. Interpret in words the confidence interval you calculated in part b above. [3 marks] d. How might this researcher's sampling methodology result in a violation of the independence assumption for inference and why? [3 marks] e. In your own words, write one sentence to describe what happens to the precision of a confidence interval when we increase the confidence level. [2 marks] f. Next, imagine that the researcher was able to conduct a new survey with a sample size that is ten times larger (n=2,140). Assuming the same proportion of students use fast fashion, recalculate the upper and lower bounds of the 95% confidence interval for the new sample. Write one sentence to describe what has changed in the confidence interval and why. [6 marks] g. Write one or two sentences to describe why is it good practice to use confidence intervals to communicate uncertainty when estimating a population proportion. [3 marks] ENG US acer SWIFT F4 F5 F6 F7 F8 F9 F10 F11 F12