Question 1 You are interested in the question whether working besides studying leads to a lower chance of passing. You have information containing the grades of all students in a large introductory statistics course as well as whether these students did work while taking the course. Derive and compare the probability that a student failed the course when she or he was working with the same probability for those that were not working.
Question 2 You believe that 40 % of students in Australia work next to their studies. Determine the number and share of students enrolled in tutorial 1 that work next to their studies. Then do the same for the whole course. Calculate the probabilities that you do observe exactly the calculated numbers (not shares) of working students in tutorial 1 respectively the whole course, given the probability stated above. Shortly discuss what assumptions you made in your calculations and what you observe about the results.
a) If you believe that final grades were randomly distributed following the uniform distribution, how many students do you expect to fail the course next year? Explain your reasoning.
b) Explain and conduct a check of the data, which has to make use of a chart, to see if the assumption of a uniform distribution for the final grades is valid. If not, determine a more appropriate distribution for the final grades, including deriving the mean and standard deviation. Then use this information to calculate the probability that a student might fail this course next year.
a) James was the tutor of tutorial 21. However, he is interested in the outcome of the overall course. To help him out, you use the information for tutorial 21 to calculate two point estimates of the average grade for the whole course using two different ways. Explain if you expect the two estimates to be the same.
b) Then calculate an interval estimate for the average grade using the information from tutorial 21. If you need any further information besides that given, you are free to select it as you wish as long as you shortly explain your choice. Explain the result and discuss which assumptions you made and how these could be justified.