(12 points) On the day before homework submission deadline, I found that last year 39 out of 94 students submitted their homework. I want to see if HMFG students are any different from the overall students, I looked at the submission of the HMFG students and found that 6 out of 18 students submitted their homework a day before deadline. a. Formulate the null and alternative hypothesis. b. Compute the p-value for the hypothesis test that can determine if the proportion of students who submitted their homework a day before the deadline are any different from the whole class. c. Using a = 0.05 signicance level, what is your conclusion about HMFG students and the overall students? Show it diagrammatically. (10 points) Green tea Co. is selling their tea in bottles. Their new bottling machine need to ll their bottles into 160ml of green tea. They need to test the machine with the hypothesis as follows: How S 160 lett > 160 Let's assume that they randomly took a sample of 30 bottles and we know the population standard deviation to be 8. With a: = 0.05. a. What would it mean to make a Type 11 error in this situation. b. What is the probability of making a Type 11 error when the machine is overlling by Sml