2. Able-bodied carpenter Dorabella eagerly xes gargantuan houses in joyful Knot's Landing, making nothing overly perfect, quite rightly she torments unbearable vigilantes, wicked xenophobes, young zealots, and bad carpenters. On her last 25 Projects Dorabella has earned a total of $30,864. POINTS a. Estimate Dorabella's Mean Earnings for the Population of all her Projects. (5) b. To draw any inferences from these data, what must we assume about the Population of Dorabella's Project Earnings, and why? (10) c. For Dorabella's Sample of 25 Projects, suppose that s = $125. i. Find a 90% Condence Interval for her Population Mean Earnings. ii. Find a 99% Condence Interval for her Population Mean Earnings. iii. Compare your intervals in c.i. and c.ii.: which is wider, and why? U'U'U' V'sV . What Hypotheses should Dorabella use to test that she can rake in more than $1200 per Project, on average? Dene in words any parameters. (15) . To test these Hypotheses, what TestStatistic should Dorabella use? (5) What is its Sampling Distribution under Null Hypothesis Hg? (5) Find the P-value for your test, state your conclusions at or : 0.05, (10) and interpret the result. Is it consistent with your intervals in c.? (10) . If Dorabella believes that actually a = $120 for her entire Population of Projects, how does this change your answers to parts b. f. ? i. What must we assume about our Sampling Population, and why? (10) ii. Find 90% $5 99% Condence Intervals for Dorabella 8 Mean Earnings. (10) How do these intervals compare to your intervals in part c., and why? (10) ) iii. What Hypotheses should Dorabella use to test if ,a 2 $1200? (10 Dene in words any parameters that you use. iv. What TestStatistic should Dorabella use to test these Hypotheses? (5) What is its Sampling Distribution under Null Hypothesis H0? (5) v. Find the P-value for this test, state your conclusions at a = 0.05, (10) interpret your result, and compare it with your intervals in g.ii. (10) vi. Explain how and why your test results change. (10) . Use a: $1225 and cr $120 to estimate probabilities that Dorabella' s: i. M can Earnings from a 25 Projects exceeds $1200. (10) ii. Total Earnings from 100 Projects exceeds $125,000. (10) . If 0 = $120, how large a Sample would Dorabella need to estimate her Mean Project Earnings to a: i. 96% error margin of $25? ii. 98% error margin of $15? iii. Compare your answers and explain their difference