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.022 0.022(Round to 3 decimal places)Question 3. What is the probability that the proportion of these 400 freshmen that return to the same school for their
ST 350-002 HW #8 Spring 2016[4/27/2016 11:36:43 AM]3.2/2 points| PreviousAnswersMy Notes4.3/3 points| PreviousAnswersMy Notessophomore year is less than 0.68?.0115 0.0115(Round to 4 decimal places) Solution or ExplanationNOTE: The solutions shown below assumes that the Department of Education proportion of college freshmen that returnfor their sophomore year is p = 0.70 and the size of the random sample is n = 450. The proportion in question 3 isassumed to be 0.72. Your version of the problem may have different values.Question 1: E(phat) = p = 0.70Question 2: SD(phat) = sqrt[p*(1-p)/n] = sqrt[0.70*(1-0.70)/450] = 0.022Question 3: The sampling distribution model for phat is N(0.70, 0.022)P(phat < 0.72) = P[(phat-0.70)/0.022 < (0.72-0.70)/0.022] = P[z < 0.02/0.022] = P[z < 0.91] = 0.8186Just before a city referendum on a school budget, a local newspaper polls 470 voters in an attempt to predict whether thebudget will pass. Suppose that, unknown to everyone, the budget actually has the support of 54% of the voters.Question. What is the probability the newspaper's sample will lead the newspaper to predict defeat of the referendum, thatis, what is the probability that the newspaper's sample results in a sample proportion p̂less than 0.50 in favor of thereferendum?.0409 0.0409(calculate the standard deviation of p̂to 4 decimal places, round your final answer to 4 decimal places).Solution or ExplanationNOTE: the solution shown below assumes that the size of the newspaper's sample is n = 470 and that the budget has thesupport of 54% of the population, that is, p = 0.54. The values in your version of the problem may differ.E(p̂) = p = 0.54; SD(p̂) = sqrt[p*(1-p)/n] = sqrt[0.54*0.46/470] = 0.0230. So the sampling distribution model for p̂isp̂~N(0.54, 0.0230).Therefore,P(p̂< 0.50) =P[(p̂-0.54)/0.0230 < (0.50-0.54)/0.0230]=P[z < -1.74] = 0.0409The concept of sampling error is discussed in the section Understanding the Margin of Sampling Errorin the middle ofpage 4 in the document New York Times Polling Standards (pdf). The third paragraph in this section is discussing thesampling distribution of , where is the sample proportion of items in a sample that has the characteristic ofinterest.Question 1. If, as mentioned in the third paragraph, "the truth is 40%" (that is, the value of the population proportion p is
ST 350-002 HW #8 Spring 2016[4/27/2016 11:36:43 AM]5.2/2 points| PreviousMy Notesp = .40), select the choice below that represents the sampling distribution model for based on a sample of size n =1000.It may assist you in answering the following questions to first verify the statement made in the last sentence of the thirdparagraph: "And 95 out of those 100 separate poll measures would be between 37% and 43%". Recall that the populationproportion p is .40 and n = 1000.