Problem 1: Mars Landing (no data set) A sample of 830 Americans was randomly selected on the population of all American adults. Among other questions, the sample was asked if they believe that the United States will land a human on Mars by 2050. Of those sampled, 544 stated that they believe this will happen. a) Calculate the sample proportion of Americans who believe the US will land a human on Mars by 2050. Round this value to four decimal places. b) Write one sentence each to check the three conditions of the Central Limit Theorem. Show your work for the mathematical check needed to show a large sample size was taken. c) Using the sample proportion obtained in (a), construct a 90% condence interval to estimate the population proportion of Americans who believe the US will land a human on Mars by 2050. Please do this \"by hand" using the formula and showing your work (please type your work, no images accepted here). Round your condence limits to four decimal places. (1) Verify your result from part (c) using Stat 9 Proportions Stats 9 One Sample 9 With Summary. Inside the box, enter the number of successes, the number of observations, select condence interval, set it to the correct level, and click Compute! Copy and paste your StatCrunch result in your document. e) Interpret the StatCrunch condence interval in part (d) in one sentence using the context of the question. 1) Use the Condence Interval applet (for a Proportion) in StatCrunch to simulate