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##### STATS Assignment Paper

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Question;INSTRUCTIONS;Read every question carefully. Write your answers and calculations legibly.;Your work must be shown to receive full credit.;Underline your final answer.;Put your name on top of the first problem.;Use three (3) decimal places of accuracy unless;instructed otherwise.;Name;Problem;1 (25 points): The safety director of an;insurance company took samples at random from his minor accidents file and;classified them according to the time the accident took place.;Number;Time of;Accidents;8 - 9 am 6;9 - 10 am 6;10;- 11 am 20;11;- 12 am 8;1 - 2;pm 7;2 - 3;pm 8;3 - 4;pm 19;4 - 5;pm 6;Using;the chi-square test and the.01 level of significance, determine whether or not;the accidents are evenly distributed throughout the day.;a) What are;the Null and Alternate Hypotheses?;b) What is;the critical value?;c) What is;the Decision Rule?;d) What is;the test statistic?;e) What is;the decision?;f) What;does the decision infer?;Problem;2 (25 points): Bob, a manufacturing plant manager, is inspecting the diameters;of ball bearings produced by a suspected malfunctioning unit. He randomly selects a sample of 12 ball;bearings and measures the diameters, which are as follows (in millimeters);Sample;1 152;141 148;Sample;2 150;146 156;Sample;3 155;149 153;Sample;4 156;147 151;a) Construct;a Mean Chart. Assume sample sizes of;3. Include the UCL and LCL. Is the process in control? (12.5 points);b) Construct a Range Chart. Assume sample sizes of 3. Include the UCL and LCL. Is the process in control? (12.5 points);Problem;3 (25 points): A Los Angeles utility;needs to decide whether to invest 5 billion dollars to build a new power plant;in 1995. Its current plants produce a;total of 5400 Megawatts (MW) of electricity.;The actual peak electrical demand of the Los Angeles area since;1980 is shown below.;Actual;Peak;Year Demand;(MW);1980 4,069;1981 4,364;1982 4,456;1983 4,445;1984 4,882;1985 4,713;1986 4,742;1987 4,922;1988 4,991;1989 4,774;1990 5,312;1991 5,100;a) What is;the Linear Trend equation for this data?;(15;points);b) Plot the;straight line developed from the Linear Trend equation, and the actual Peak;demand versus the time, with time being the independent variable.;(5 points);c)What;is the projected demand for 1995? (5 points);Problem 4 (25 points): A manufacturing company has;\$100,000 available to invest. Doctor;Goodbuy, the president and CEO of the company, would like to either expand his;production, invest the money in stocks, or purchase a certificate of deposit;from the bank. Of course, the unknown is;whether the economy will continue at a high level or there will be a;recession. He estimates the likelihood;of a recession at 20%. Whether there is;a recession or not, the certificate of deposit will result in a gain of 6;percent. If there is a recession, he;predicts a 10 percent loss if he expands production and a 5 percent loss if he;invests in stock. If there is not a;recession, an expansion of production will result in a 15 percent gain, and;stock investment will produce a 12 percent gain (Use only the amount made or;lost in the answers).;1) Develop a payoff table for the various acts;and states of nature. (6 points);2) Compute the total expected payoff for each;alternative.;(6 points);3) Construct an Opportunity Loss Table.(6;points);4) What is the lowest total expected Opportunity;Loss?;(2 points);5) What decision should Doctor Goodbuy make? (2;points);6) What is the maximum amount that Doctor;Goodbuy should pay to a consultant for financial advise for this scenario (in;other words, what is the EVPI?) (3 points)

Paper#61513 | Written in 18-Jul-2015

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