Applic. - Case Study - estimation - Case Study The Bureau of Labor Statistics collects data on employment and hourly earnings in private industry groups

Applic. - Case Study - estimation - Case Study The Bureau...

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1 Case Study The Bureau of Labor Statistics collects data on employment and hourly earnings in private industry groups and publishers its findings in Employment and Earnings . Twenty people working in manufacturing industry are selected at random: their hourly earnings, in dollars, are as follow: 16,70 7,44 13,78 16,49 7,49 17,92 17,21 5,51 10,40 10,75 15,27 19,72 10,68 13,10 14,70 15,55 16,67 15,07 14,02 15,99 Find 95% confidence interval for the mean hourly earnings, of all people employed in the in manufacturing industry. Assume the population standard deviation of the hourly earnings is $3,25. What is the margin error? Case Study In 1908 William S. Gosset published the article “ The Probable Error of the Mean ” ( Biometrika, Vol.6, pp.1-25 ). It is in this pioneering paper, published under the pseudonym “Student”, that he introduced what later became known as Student’s t -distribution . As an example, Gosset used following data set, which gives the additional sleep in hours obtained by 10 patients using laevohysocyamine hydrobromide . 1,9 0,8 1,1 0,1 -0,1 4,4 5,5 1,6 4,6 3,4 Find 95% confidence interval for the additional sleep that would be obtained on the average for all people using laevohysocyamine hydrobromide . Does it appear that the drug is effective in increasing sleep?
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2 Case Study Forbes (January 3, 1994) gave the following data about percentage return on capital (12 months) for representative stocks in the entertainment/information sector. Stocks such as CBS, Turner Broadcasting, Walt Disney, Time Warner, Gannet, and so on were included. 29,7 21,1 6,5 10,0 9,0 3,6 2,4 23,5 9,3 9,7 10,6 5,5 12,3 1,7 22,0 21,7 28,9 26,9 14,9 13,7 9,6 2,3 7,1 12,9 10,3 10,9 8,1 8,1 10,8 8,2 7,0 11,0 10,0 5,5 3,0 4,8 6,5 19,1 17,2 4,6 14,5 Find 80% confidence interval for the average percentage return on capital for all stocks in this sector. If someone told you that the average return on capital in the entertainment/information sector was soon going to have a percentage return above 24%, would you have reason to suspect that this might not happen? Explain using the confidence interval. In the investment business, sometimes the low end of a confidence interval is called a support ( the quantity is not likely to go below this value ). The high end of a confidence interval is called a resistance ( the quantity is not likely to rise above this value ). Find a support and a resistance value for 90% credibility. Describe the margin error. Check the relative error of this estimate.
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3 Case Study The Roman Arches is an Italian restaurant. The manager wants to estimate the average amount a customer spends on lunch Monday through Friday. A random sample of 115 customers’ lunch tabs gave a mean of $9,74 with standard deviation $2,93.
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