Question 4 - Statistical Inference: Hypothesis testing and estimation [Total: 15 marks] A recent survey of 1052 random GenZ customers (a company that delivers mobile phone coverage) were asked about their satisfaction of mobile coverage, where 886 reported that they were satisfied with the mobile coverage that GenZ provides.

I. Construct a 99% confidence interval for the (population) proportion of customers interviewed and felt satisfied with their coverage. What does this indicate? [4 marks]

II. It is has been reported that the typical rate of customer satisfaction with respect to mobile coverage is less than 80%. Using the current information from the GenZ survey, test the claim that the rate of mobile coverage satisfaction significantly differs from 80%. Use all steps for hypothesis testing to make a conclusion at a significance level (alpha) of 5%. [9 marks]

III. What assumptions or conditions are made when conducting these statistical inference tests above? Are they being satisfied? If so or if not, please demonstrate. [2 marks]

Marking Criteria for Question 4: You need to show all working. No marks awarded for the correct answer without working out. For full marks, you need to demonstrate understanding of the statistical inference concepts involved in each part of this question as well as a relevant written statement with a brief appropriate interpretation at the end of each question.

Thankyou in advance