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D EPARTMENT OF E CONOMICS E CON 131 A Y ALE U NIVERSITY E CONOMETRICS & D ATA A NALYSIS I F ALL 2010 Assignment #4 Due Tuesday October 5 In Class The same rules apply as on previous assignments. You may work with a study group of your choice on this assignment. However, even if you work with others you must write up and submit your own assignment. You may do your work by hand or in Excel, and you may hand in either handwritten answers or typed answers. Your grade depends on (1) getting the answer right, and (2) showing how you arrived at a correct answer. Late assignments will not be accepted. 1. ( Opinion polls. ) An opinion poll of 4,000 (randomly selected) voters is con- ducted. The fraction of all voters in the population with an annual income above $50k is 35%. What is the chance that 1450 or more of the voters with annual incomes above $50k will be polled? 2. ( Sample probabilities mechanics. ) The town of Hayward (CA) has about 50,000 registered voters. A political research firm takes a simple random sample of 500 of these voters. In the sample, the breakdown by party affiliation is Republican 115 Democrat 331 Independent 54 Calculate a 95% confidence interval for the true percentage of independents among Hayward’s 50,000 registered voters. 3. ( Accuracy of samples. ) A survey research company switched some years ago to random digit dialing. They have a contract to estimate the percentage of people listening to Spanish-language radio programs in several Southwest- ern cities. They are using a sample size of 1,000 in Austin, Texas – which has about 500,000 residents. And they are satisfied with the accuracy of the estimates for Austin. (a) Dallas has about twice the population of Austin, but similar demograph- ics. True or false: to get about the same accuracy in Dallas as in Austin, the company should use a sample size of 2000. 1
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(b) How would you explain your answer to an interested station manager without any training in statistics? 4. ( More sample probabilities mechanics. ) An airline does market research survey on travel patterns. It takes a simple random sample of 225 people aged 18 and over in a certain city, and works out the 95% confidence interval for the average distance they traveled on vacations in the previous year. This was 488 to 592 miles.
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