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The StatCom organization of Stratified University conducted a sample survey of un- dergraduate students to obtain the opinions on statistics. Among the 1000 sampled students, 87% majored in science or engineering and 13% majored in other subjects. It is known from administration that the university has approximately 75% science or engineering major students and 25% other major students. One of the questions asked was Do you think learning statistics is helpful for your future career? The accompanying table shows a summary of the responses by major group. Yes No Total Science or Engineering major 696 174 870 Other major 26 104 130 Total 722 278 1000 a. Assuming that the 1000 responses came from a stratified random sample of un- dergraduate students, estimate the true proportion of students who would answer "yes" to this question. Calculate an appropriate margin of error. b. Assuming that the 1000 responses came from a simple random sample of under- graduate students, estimate the true proportion of students who would answer "yes" to this question. Calculate an appropriate margin of error. c. Assuming that the 1000 responses came from a simple random sample of under- graduate students, construct a poststratification estimate of the true proportion of "yes" answers among undergraduate students, with an appropriate margin of error. Comment on whether or not poststratification pays any dividends in this situation