(1] The University of Edinburgh wants to evaluate how many employees have returned to campus after the easing of Covid restrictions. A survey of 45 randomly selected lecturers within the School of Mathematics found that 32 had returned to campus whilst the others continue to work from home. State whether each of the following statements is either 'true', 'false' or 'may be true or false'. Fully justify your answer. (a) In a statement, the University Chancellor says that 29% of all university employees are working from home. [4 marks] (in) Let 36 he the sample proportion of mathematics lecturers who have returned to campus. In statistics, the uncertainty in this estimate comes hum the fact that the true proportion, p, is unknown. [4 marks] (c) The calculation 1 335 represents the maximum likelihood estimate for the probability that at least one employee on a corridor of 6 mathematics lecturers is working from home. [4 marks] (d) By assuming that the survey sample size is suiciently large, an approximate condence interval for p is (63%., 88%) rounded to the nearest whole percent. [4 marks] (e) The head of the school claims that that the actual proportion of returned lecturers in the school is 80% or higher. To support this claim, the head of the school has provided the following calculation and states that this p-value is smaller than the 5% signicance level. dbinom{32, size = 45, prob = 0.8) [1] 0.04738374 [4 [marks]