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1. In Quiz 1 you were required to select a random sample of 36. To make the population I printed everything out, and then I manually cut all of the paper into small pieces so that each small piece of paper had one observation. In the manual process of cutting the paper some of the small pieces of paper were quite a bit larger than other pieces of paper (part of the reason is because I didn’t take much care when cutting, and the other is the page margins). Let’s assume that larger pieces of paper are more likely to be selected. Does this selection bias indicate that the sample average is a biased estimator of the population mean? Please explain in which cases the estimator would be biased, and when it would not be biased. (5) 2. The following are the probabilities and prizes for winning the Powerball lottery. Assume that the Grand Prize is $80 Million. a. What are the expected winnings? (3) b. The price of a ticket is $2. How large would the Grand Prize have to be in order for the expected winnings to be equal to the ticket price? (3) 3. In making long term business decisions it is important to take the state of the economy into consideration. The problem is that the state of the economy is always changing. Over the recorded history of the united states the mean annual GDP growth rate is 2%, with a population standard deviation of 1.6% and is normally distributed. a. What is the 99% confidence interval on the annual growth rate of U.S. GDP? (3 b. You are involved in a long run hospital construction project. What is the probability that in the year the project is completed that the U.S. GDP growth will be negative? (3) 4. Consider the recent article ‘Alcohol use and burden for 195 countries and territories, 1990–2016: a systematic analysis for the Global Burden of Disease Study 2016.’ a. Based on the article, what is the safe amount of alcohol? (2) b. How many other empirical datasets are included in the analysis? (2) c. What sources of bias do the authors purport to correct in the study? (3) d. What kind of data are the authors using in their analysis? More particularly, are they using experimental data or observational data? (2) e. Based on type of data they are using, is there anything that is causal about the work in this paper? (5)

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1.         Yes, since larger pieces are more likely to be selected, therefore sample average are likely to be biased and it could be dependent on large size pieces because every time we have high chances to choose large size pieces. In we choose small sample size or repeat sampling less number of times. Then estimator will be based. But if we take population size is large and repeat number of times experiment. In that case sample could be unbiased...

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