Data Management, Analysis and Reporting

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Complete Chapter 4 problems 67 and 78 from page 204 and 206 at the end of the chapter. Within each spreadsheet, include a brief explanation of what the data is telling you. I've attached the excel files that contain the data to solve the question and I've highlighted the questions.

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Salary data Salary Increase $0 $0 $0 $0 $2,000 $2,000 $2,000 $2,000 $4,500 $4,500 $4,500 $4,500 Merit Rating 0 1 2 3 0 1 2 3 0 1 2 3 Probability 0.08 0.1 0.05 0 0.06 0.2 0.2 0.02 0.01 0.1 0.1 0.08 Means and standard deviations of weekly production (units produced) of two products Product Mean Standard deviation X 22500 2500 Y 30000 3350 64. A roulette wheel contains the numbers 0,00, and 1 to 36. If you bet $1 on a single number coming up, you earn $35 if the number comes up and lose $1 otherwise. Find the mean and standard deviation of your winnings on a single bet. Then find the mean and standard deviation of your net winnings if you make 100 bets. You can assume (realistically) that the results of the 100 spins are independent. Finally, provide an interval such that you are 95% sure your net winnings from 100 bets will be inside this interval 65. Assume that there are four equally likely states of the economy: boom low growth, recession, and depression. Also, assume that the percentage annual retwn you obtain when you invest a dollar in gold or the stock market is shown in the file P04_65.xlsx. a. Find the covariance and correlation between the annual return on the market and the annual retun on gold. Interpret your answers. b. Suppose you invest 40% of your available money in the market and 60% of your money in gold Determine the mean and standard deviation of the annual retun on your portfolio. c. Obtain your pat b answer by determining the actual return on your portfolio in each state of the economy and then finding the mean and variance calculating the return on your portfolio for each state and use the formulas for mean and variance of a random variable. For example, in the boom state, your portfolio eams 0.25(0.25) + 0.75(0.32). 67. Each year the employees at Zipco receive a $0, $2000, or $4500 salary increase. They also receive a merit rating of 0, 1, 2 or 3, with 3 indicating outstanding performance and 0 indicating poor performance. The joint probability distribution of salary increase and merit rating is listed in the file P04_67.xlsx. For example, 20% of all employees receive a $2000 increase and have a merit rating of 1. Find the corre- lation between salary increase and merit rating. Then interpret this correlation 68. The return on a portfolio during a period is defined by PV - PV PV bag where PV is the portfolio value at the beginning of period and PT od is the portfolio value at the end of the period. Suppose there are two stocks in which you can invest, stock 1 and stock 2. During each year there is a 50% chance that each dollar invested in stock I will turn into $2 and a 50% chance that each dollar invested in stock 1 will turn into $0.50. During each year there is end bes 78. A manufacturing plant produces two distinct products, A and B. The cost of producing one unit of A is $18 and that of B is $22. Assume that this plant ineus a weekly setup cost of $24,000 regardless of the number of units of A or B produced. The means and standard deviations of the weekly production levels of A and B are given in the P04_78.xlsx. a. Assuming that the weekly production levels of A and B are independent, find the mean and standard deviation of this plant's total weekly production cost. Between which two total cost figures can you be about 68% sure that this plant's actual total weekly production cost will fall? b. How do your answers in part a change if you discover that the correlation between the weekly production levels of A and B is actually 0.29? Explain the differences in the two sets of results. 79. The typical standard deviation of the annual retun on a stock is 20% and the typical mean retun is about 12%. The typical correlation between the annual retuns of two stocks is about 0.25. Mutual finds often put an equal percentage of their money in a given number of stocks. By choosing a large member of stocks, they hope to diversify away the risk involved with choosing particular stocks. How many stocks does an investor need to own to diversify away the risk associated with individual stocks? To answer this question, use the above information about "typical” stocks to determine the mean and standard deviation for the following portfolios: • Portfolio 1: Half your money in each of 2 stocks Portfolio 2: 20% of your money in each of 5 stocks Portfolio 3: 10% of your money in each of 10 stocks Portfolio 4: 5% of your money in each of 20 stocks Portfolio 5: 1% of your money in each of 100 stocks What do your answers tell you about the number of stocks a mutual fund needs to invest in to diversify adequately? standard deviation of their net winnings. The file gets you started a. Player 1 always bets on red. On each bet, he either wins or loses what he bets. His first bet is for $10. From then on, he bets $10 following a win, and he doubles his bet after a loss. (This is called a martin- gale strategy and is used frequently at casinos.) For example, if he spins red, red, not red, and not red, his bets are for $10, 10, $10, and $20, and he has a net loss of $10. Or if he spins not red, not red not red, and red, then his bets are for $10, $20, $40, and $80, and he has a net gain of $10. b. Player 2 always bets on black and green. On each bet, he places $10 on black and $2 on green If red occurs, he loses all $12. If black occurs, he wins a net $8 ($10 gain on black $2 loss on green). If green occurs, he wins a net $50 ($10 loss on black, $60 gain on green). 82. Suppose the New York Yankees and Philadelphia Phillies (two Major League Baseball teams) are playing a best-of-three series. The first team to win two games is the winner of the series, and the series ends as soon as one team has won two games. The first game is played in New York, the second game is in Philadelphia, and if necessary the third game is in New York. The probability that the Yankees win a game in their home park is 0.55. The probability that the Phillies win a game in their home park is 0.53. You can assume that the outcomes of the games are independent a. Find the probability that the Yankees win the series. b. Suppose you are a Yankees fan, so you place a bet on each game played where you win $100 if the Yankees win the game and you lose $105 if the Yankees lose the game. Find the distribution of your net winnings. Then find the mean and standard deviation of this distribution. Is this betting strategy favorable to you? c. Repeat part a, but assume that the games are played in Philadelphia, then New York, then Philadelphia. How much does this "home field LTL12
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Explanation & Answer

Hello! I have attached the answer in word document for you.
:) Let me know if you have any further questions. All the calculations and formulae are in excel.

Last Name 1

Name
Instructor's name
Course
Date
Statistics
67. Each year the employees at Zipco receive a $0, $2000, or $4500 salary increase. They also
receive a merit rating of 0, 1, 2, or 3, with 3 indicating outstanding performance and 0 indicating
poor performance. The joint probability distribution of salary increase and merit rating is
listed in the file P04_67.xlsx. For example, 20% of all employees receive a $2000 increase and
have a merit rating of 1. Find the correlation between salary increase and merit rating. Then
interpret this correlation.
Solution
The correlation between salary increase and merit rating was calculated in excel and found
as follows:
Table 1: Calculation of Correlation

Salary data
Calculating correlation
(Salary

Analysis

Salary Inc.

Merit Rt.

1.4

Salary

Merit

(Merit

Increase

Rating

Probability increase)^2

rating)^2

E(x)

2265

$0

0

0.08

0

0

E(x^2)

1.704...


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