WEEK FIVE ASSIGNMENT QUESTION 1 The maxim um temperatures measured at the Townsville airport in 2015 from 20th May to the 31st May, sorted in ascending order and in Celsius, are 25.3, 25.8, 26.5, 27.0, 27.4, 28.5, 28.5, 28.8, 28.9, 28.9, 29.2, 30.6 3. Produce a plot of these data. Interpret. b. Using this sample, estimate with the help of R the standard error of the mean maxim um tem perature for May in Townsville. c. Using 'pen-and-paper' showhowR computed this answer. Hint 1: write the equation for the mean and substitute the numbers into this equation to show how the mean was computed. Hint 2: write the equation for the (sample ) standard deviation Ss and substitute numbers into this equation to showhowthe standard deviation was com puted. Hint 3: com bine hints 1 and 2 to showhowthe SEM was computed. d. Is the SEM that you computed a valid estimate for the SEM maximum temperature for May in Townsville? Explain your reasoning e. Answer True or False. If the answer is False rewrite it so it is True. The SEM tells us how much the meany y varies from population to population. Note the size of each population must be the same. QUESTION 2 This assignment question should be com pleted with pen and paper and by using your Z-tables. You can use R in addition to this if you are keen, but the R part is optional, the 'pen-and-paper' part is compulsory. For women aged between 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1 (based on National Health Surveys). Hypertension is commonly defined as a systolic blood pressure above 140. a. Sketch the PDF of systolic blood pressure for women aged between 18-24. b. If a woman between the ages of 18-24 is randomly selected, find the probability that her systolic blood pressure will be greater than 140. (Hint: shade this area on your PD F). C. If 4 women in that age bracket are randomly selected repeatedly, sketch the PDF of mean systolic blood pressure. d. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140. (Hint: shade this area in on your PDF) e. Given that the previous question only has a sample size of 4, explain how the Central Limit Theorem contributes to the solution