1. Let X1,. Xn are iid Bernoulli (0) random variables. = = 00 versus Ha :...

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1. Let X1,. Xn are iid Bernoulli (0) random variables. = = 00 versus Ha : 0>00. 00 versus Ha: 0 # 00. (a) Find a level a large sample likelihood ratio test for testing Ho : 0 (b) Find a level a large sample likelihood ratio test for testing Ho : 0 (c) Suppose that in a survey of 90 people from the university campus, 68 people supported legalizing abortion. Let 0 be the probability that a randomly chosen subject from the university campus supports legalizing abortion. Apply the above results of a) to test i) Ho: 0 = 0.6 versus Ha : 0 > 0.6 at the 5% level, ii) by inverting the test construct a 95% CI for 0, iii) calculate the power of the test when : 0.65, iv) calculate the power of the test when 0 = 0.7, v) what would be the required sample size if we want 90% power when = 0.7. = (d) Suppose that in a survey of 80 people from the university campus, 35 favor the university not receiving corporate funding. Let 0 be the probability that a randomly chosen subject from the university campus supports the university not receiving any corporate funding. Apply the above results of b) to test i) H0 : 0 = 0.5 versus Ha: 00.5 at the 5% level, ii) by inverting the test construct a 95% CI for 0, iii) calculate the power of the test when = 0.45, iv) what is the power of the test when : 0.5, v) what would be the required sample size if we want 90% power when 0 = 0.55. = 1. Let X1,. Xn are iid Bernoulli (0) random variables. = = 00 versus Ha : 0>00. 00 versus Ha: 0 # 00. (a) Find a level a large sample likelihood ratio test for testing Ho : 0 (b) Find a level a large sample likelihood ratio test for testing Ho : 0 (c) Suppose that in a survey of 90 people from the university campus, 68 people supported legalizing abortion. Let 0 be the probability that a randomly chosen subject from the university campus supports legalizing abortion. Apply the above results of a) to test i) Ho: 0 = 0.6 versus Ha : 0 > 0.6 at the 5% level, ii) by inverting the test construct a 95% CI for 0, iii) calculate the power of the test when : 0.65, iv) calculate the power of the test when 0 = 0.7, v) what would be the required sample size if we want 90% power when = 0.7. = (d) Suppose that in a survey of 80 people from the university campus, 35 favor the university not receiving corporate funding. Let 0 be the probability that a randomly chosen subject from the university campus supports the university not receiving any corporate funding. Apply the above results of b) to test i) H0 : 0 = 0.5 versus Ha: 00.5 at the 5% level, ii) by inverting the test construct a 95% CI for 0, iii) calculate the power of the test when = 0.45, iv) what is the power of the test when : 0.5, v) what would be the required sample size if we want 90% power when 0 = 0.55. =