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Question 1) In 2004 it was reported that 31% of all graduating US college students were graduating with STEM degrees (Science Technology Engineering and Math). You want to study if this percentage has increased. To study this you divide the country into 4 major regions, East Coast, Midwest, South, and West Coast and randomly sample 70 students from each region. This means you ultimately randomly sample 280 graduating students and find that 95 of them were graduating with STEM degrees. (a) Carry out at (r = .05 a hypothesis test to test the claim that the percentage of US college students that get STEM degrees has increased since 2004. Make sure to check all necessary condi- tions and state your conclusion in the context of this problem. (b) Build a 95% condence interval to estimate the current percentage of US college students that graduate with a STEM degree. Make sure to check any necessary conditions and interpret your interval in the context of this problem. (c) What type of sampling did you use to build your sample? EXTRA CREDIT QUESTION (2 points) Look back at Question 1. Suppose that as a follow up question you asked all the students who were graduating with STEM degrees if they planned on working in academia. Out of the 95 students graduating with STEM degrees, 9 report they plan on working in academia. Build a 95% condence interval for the true percentage of students graduating with STEM degrees that plan on working in academia. Make sure to interpret your interval and check any necessary conditions. (Hint: Make sure to use an appropriate method to do this)