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Individual assignments Subject: MANAGEMENT DECISION MAKING Question 1: S & P 500 is a very large group of 500 companies listed in the United States In 2006, the average annual return of the stocks in the S & P 500 was 13.62% with a standard deviation of approximately 20% According to historical data, profits of this stock has a normal distribution Use the above parameters to evaluate a number of possibilities by answering the following questions a Possibility (probability) to a share of the S & P 500 will gain at least 25%, at least 50%? b Possibility (probability) to a share of the S & P 500 lost at least 25%, at least 50%? c Use sigma principles for a stock in the S & P 500 will have profit and loss fluctuations like? Note: For each question, students use the blanket Megastat to exercises, the student is not clear how to use and make data and software After putting the data into the software to calculate, students use the results calculated by software included in the exercises to answer each question Assignments a Possibility (probability) to a share of the S & P 500 will gain at least 25%, at least 50%? I use the blanket Megastat to answer questions From software to the Probability / Normal Distribution then enter the data into the table we have the following result 1.1 Possibility (probability) to a share of the S & P 500 will gain at least 25% Theo ta có: µ = 13.62; চ = 20 Normal distribution P(lowe r) 7157 P(uppe r) 2843 z 0.57 X 25 mean 14 std.de v 20 Thus we have the possibility (probability) to a share of the S & P 500 will gain at least 25%, P = 0.2843 Possibility (probability) to a group neck phie in the S & P 500 will gain at least 50% 1.2 Tính khả (xác suất) để cổ phiế nhóm S&P 500 thu lợi 50% Normal distribution P(lowe r) 9656 P(uppe r) 0344 z 1.82 X 50 mean std.dev 14 20 We have the ability (probability) to a share of the S & P 500 will gain at least 50%, P = 0.0344 a Possibility (probability) to a share of the S & P 500 lost at least 25%, at least 50%? 2.1 The possibility (probability) to a share of the S & P 500 lost at least 25% Normal distribution P(lowe r) 0268 P(uppe r) z 9732 -1.93 X -25 mean 14 std.de v 20 We have the ability (probability) to a share of the S & P 500 lost at least 25% is P = 0268 2.2 The possibility (probability) to a share of the S & P 500 lost at least 50% Normal distribution P(lowe r) 0007 P(uppe r) 9993 z -3.18 X -50 mean std.dev 14 20 We have the ability (probability) to a share of the S & P 500 will be at a loss of at least 50%, P = 0.0007 c Use sigma principles for a stock in the S & P 500 will have profit and loss fluctuations like? We have μ - Ϭ = 13.62 - * 20 = - 46.38 μ + Ϭ = 13.62 + * 20 = 73.62 Let X be the income, we have P (μ - Ϭ μ + Ϭ), so that we can return to a profit and loss shares will be in the range of (μ - Ϭ μ + Ϭ ) f(z) z -3.00 -3 -2 -1 3.00 Normal distribution P(low er) P(upp er) z X mean std.de v 0013 9987 -3.00 46.38 13.62 20.00 9987 0013 3.00 73.62 13.62 20.00 We have the probability P = 0.9987 number of stock losses and profits are in the range 46.38 to 73.62 Question A market research for an electronics company to investigate the TV viewing habits of the population in a region A random sample of 40 survey respondents and obtained the following results: - The average time watching TV one week of 40 is 15.3 hours and the standard deviation is 3.8 hours - Of the 40 people, 27 people watching the show "Who Wants to be a Millionaire" during the week a Construction 95% confidence interval for the average TV viewing time per week of local people b Is it the average TV viewing time has increased over the past years (under investigation average time watching TV 13go week (use hypothesis testing to check) c Find the 95% confidence interval for the percentage of people watching the show "Who Wants to be a Millionaire" Explain the significance of the findings Suppose researchers want to perform in one area of investigation Said: d That need to get as many people to investigate that with 95% reliability will estimate the average time watching TV deviation less than hours around the sample average (assuming the overall standard deviation of hours ) e How many people need to investigate if you want to estimate the proportion Son gười View program "Who Wants to be a Millionaire" with a 95% confidence level and margin of error 0.035) a Construction 95% confidence interval for the average TV viewing time per week of local people From software Megastat a / Confidence Interals / Sample Size-approaches, given the data we have the following result Confidence interval - mean 95% 15.30 3.80 40.00 1.960 1.178 16.478 14.122 confidence level mean std dev n z half-width upper confidence limit lower confidence limit Reliability of 95% of the time watching TV in an average week of people in the area from 14,122 hours to 16,478 hours b Is it the average TV viewing time has increased over the past years (when chronological survey view TV average 13giờ week (using hypothesis testing to check) We use hypothesis testing methods From software Megastat / hypothesis Tests / Meanve Hypothesized Value, put the data in the following table Hypothesis Test: Mean vs Hypothesized Value 13.00 15.30 3.80 0.60 40.00 3.83 0.0001 hypothesized value mean thoi gian std dev std error n z p-value (one-tailed, upper) Conclusion: We have P-value