Suppose of the 45 additional student surveyed, 31 said 'yes' to enrolling into the sport analytics elective. If the university decided on a prior of (10,5) prior for p, what is the posterior distribution of p?

Now suppose that based on the popularity of similar electives, the university expects a high proportion of students to enrol, with p most likely around 0.8. Which of the following priors best reflects this belief?

Using the information provided in Q9, what is the posterior mean of p, the probability that a student would enrol? 

• Report your answer in decimal format, rounded to 2 decimal places without units. (e.g. X.xx)

Before examining the survey results, the university wants to select a prior for p, the probability that a student would enrol. If they have no idea whether p is low, high or somewhere in between, and want every value between 0 and 1 to be equally plausible, which of the following priors is most appropriate?

Based on the QQ plots below, which statement best summarises how well the candidate distributions fit the completion_time data?

Construct a plot to visualise the distribution for completion_time. Which of the following best describes the distribution?

Why might the normal distribution be a poor candidate for modelling completion_time? (Hint: have a look at your plot in Q1)

Calculate the difference in log-likelihood between the strongest and weakest models (based on log-likelihood). 

• Report the absolute difference. 
• Round your answer to two decimal places.

Fit five different models to completion_time:

• normal
• exponential
• gamma
• weibull
• lognormal

Which model has the lowest loglikelihood, and what does this mean?

Save your quarto document and upload it here. Make sure you are uploading the quarto document that contains your code, and not the blank file you downloaded. Tip: Save it with a different name (e.g. lastname_firstname_quiz2)

• Failure to provide your quarto document may result in a 0 for this test.