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name: Mathematics 146 tenth homework due Monday, November 30, 2015 1. The claim is made that the mean I.Q. of students at a college is equal to 118. It is known that the population standard deviation of all the student I.Q.s is equal to 5. A sample of one hundred randomly selected students’ I.Q.s are collected. The sample mean is found to be 119. Assuming that the I.Q.s in the college are normally distributed, (a) write down the null & alternate hypotheses in this case (b) What is the P -value of the sample (mean) statistic ? (c) with level of signifigance α = 0.04, what would you conclude about the original claim ? (d) construct a 96% confidence interval for the college students’ mean I.Q. score. 2. A pollster states that a majority of a city’s voters will vote for a new stadium. A random sample of 400 voters found that 53% would vote for the new stadium. (a) write down the null & alternate hypotheses in this case (b) sketch the rejection region corresponding to level of significance α = 0.05. Include any critical value(s) in the sketch. (c) with level of signifigance α = 0.05, what would you conclude about the original claim ? (d) construct a 90% confidence interval for the population proportion in favor of building the new stadium.