Discussion Board Forum 1/Project 2 Instructions

Standard Deviation and Outliers

Thread:

For this assignment, you will use the Project 2 Excel Spreadsheet to answer the questions below. In each question, use the spreadsheet to create the graphs as described and then answer the question.

Put all of your answers into a thread posted in Discussion Board Forum 1/Project 2.

This course utilizes the Post-First feature in all Discussion Board Forums. This means you will only be able to read and interact with your classmates’ threads after you have submitted your thread in response to the provided prompt. For additional information on Post-First, click here for a tutorial. This is intentional. You must use your own work for answers to Questions 1–5. If something happens that leads you to want to make a second post for any of your answers to Questions 1–5, you must get permission from your instructor.

1. A. Create a set of 5 points that are very close together and record the standard deviation. Next, add a sixth point that is far away from the original 5 and record the new standard deviation.

What is the impact of the new point on the standard deviation? Do not just give a numerical value for the change. Explain in sentence form what happened to the standard deviation.

B. Create a data set with 8 points in it that has a mean of approximately 10 and a standard deviation of approximately 1. Use the second chart to create a second data set with 8 points that has a mean of approximately 10 and a standard deviation of approximately 4. What did you do differently to create the data set with the larger standard deviation?

2. Go back to the spreadsheet and clear the data values from Question 1 from the data column and then put values matching the following data set into the data column for the first graph.

50, 50, 50, 50, 50.

Notice that the standard deviation is 0. Explain why the standard deviation for this one is zero. Do not show the calculation. Explain in words why the standard deviation is zero when all of the points are the same. If you don’t know why, try doing the calculation by hand to see what is happening. If that does not make it clear, try doing a little research on standard deviation and see what it is measuring and then look again at the data set for this question.

3. Go back to the spreadsheet one last time and put each of the following three data sets into one of the graphs. Record what the standard deviation is for each data set and answer the questions below.

Data set 1:       0, 0, 0, 100, 100, 100

Data set 2:       0, 20, 40, 60, 80, 100

Data set 3:       0, 40, 45, 55, 60, 100

Note that all three data sets have a median of 50. Notice how spread out the points are in each data set and compare this to the standard deviations for the data sets. Describe the relationship you see between the amount of spread and the size of the standard deviation and explain why this connection exists. Do not give your calculations in your answer—explain in sentence form.

For the last 2 questions, use the Project 1 Data Set.

4. Explain what an outlier is. Then, if there are any outliers in the Project 1 Data Set, what are they? If there are no outliers, say no outliers.
5. Which 4 states have temperatures that look to be the most questionable or the most unrealistic to you? Explain why you selected these 4 states. For each state, give both the name and the temperature.

ABC Insurance Company is considering to buy reinsurance from 123 Re. There are two

types of agreement they have in mind: quota share treaty or surplus share treaty. Consider

the two policies (lines) and answer the following questions under the two types of terms of

the agreement.

Policy A insures Building A for $10,000 for a premium of $300, with one loss of $5,000.

Policy B insures Building B for $12,000 for a premium of $350, with one loss of $4,000.

a. Under a quota share treaty with a $250,000 limit, a retention of 40%, and a cession of

60%, what are the amount of insurance, premiums, and losses ABC Insurance Company

is responsible for the two policies?

b. Under a surplus share treaty where ABC retains a line of $10,000 and a maximum ces-

sion of $225,000, what are the amount of insurance, premiums, and losses 123 Re is

responsible for the two policies?

Investing (ONE PAGE FOR TWO PARTS)

For this assignment, assume that you have $10,000 to invest. Using the internet, newspapers, investing chapter presentation materials or other sources for information, select at least 2 investments, starting on any date between Jan 21 – Feb 1. You may pick any investment instruments you wish including GICs, stocks (equities), bonds, mutual funds, gold, foreign exchange futures, keeping the funds under your mattress, or any other legitimate investment as long as there are at least *TWO* different types. In other words, don’t pick 2 stocks, 2 mutual funds, or 2 GICs. If you wish, you may also “buy” and “sell” during the period to change what investments you hold, but if you do, assume a $10 transaction fee and include the detail. This is a learning exercise, so grading is based on what you think happened and what you learned. You are *NOT* being graded on whether your investments made or lost money, rather on what you learned in the process. The assignment is worth 15% of your course mark, so invest you time accordingly.

The assignment is in two parts:

First part is your starting position. Hand in on paper (one-page maximum, less is more) in the February 5 or 6 class:
1. What is your investing objective?
2. List your original investments, amount and date “bought”, and your reasons as to why each was chosen.

Second part is your ending position. Also hand in on paper (one page maximum please) in the April 2 or 3 class: Re-print the first part and add to it the following:
3. Value of investments on March 25.
4. How did your investments perform against your expectations and why do you think that happened?5. With what you’ve seen and learned in class, what investment strategy would you use in the future? Include your earlier answers to questions 1 and 2.

As a rough example (feel free to use a better or more appropriate format):
1. My investing objective is ... (include more than : “to make money” – discuss risk, why you chose the instruments you did, etc)
2. Starting Investments

3. Investments at end of period

4. My first investment gained/lost because of ... The second...

5. When I started, my strategy was to (discuss strategy and risks).... What I would do differently next time is ... and this is why: ...

For much of the past century, the conflict between Israelis and Palestinians has
been a defining feature of the Middle East. Despite billions of dollars expended to
support, oppose, or seek to resolve it, the conflict has endured for decades, with
periodic violent eruptions, of which the Israel-Gaza confrontation in the summer of
2014 is only the most recent.
This executive summary highlights findings from a study by a team of RAND
researchers that estimates the net costs and benefits over the next ten years of five
alternative trajectories — a two-state solution, coordinated unilateral withdrawal,
uncoordinated unilateral withdrawal, nonviolent resistance, and violent uprising —
compared with the costs and benefits of a continuing impasse that evolves in
accordance with present trends. The analysis focuses on economic costs related to
the conflict, including the economic costs of security. In addition, intangible costs
are briefly examined, and the costs of each scenario to the international community
have been calculated.
The economy of the Palestinian Territory was a viable and thriving one before the
occupation in June 1967. It generated significant production and income that
sustained a growing population of 1 million people and generated a gross domestic
product (GDP) per capita of about $1,349 in 2004 prices, which was sufficient for it
to be considered a lower-middle-income economy at that time. Tragically, it has
become a land on the verge of economic and humanitarian collapse.
In 2014, the GDP growth rate in the Palestinian Territory turned negative, for the
first time since 2006. The Gaza Strip is becoming increasingly unliveable and could
become totally unliveable by 2020. According to the Palestinian Central Bureau of
Statistics, the unemployment rate in Gaza was 45 per cent in 2014, with over 63
per cent of Gaza’s young people unemployed, which is the highest rate in the world.
Female unemployment in the Palestinian Territory was around 40 per cent and
more than 60 per cent in Gaza. Nearly 40 per cent of Palestinians live below the
poverty line. Clean water is a rarity, with at least 90 per cent of Gaza’s water supply
unfit for human consumption. Electricity in Gaza is also sporadic and unreliable,
available only four to six hours a day, and a properly functioning sewage treatment
system no longer exists.
Seven key findings were identified (1): A two-state solution provides by far the best
economic outcomes for both Israelis and Palestinians. Israelis would gain over two
times more than the Palestinians in absolute terms — $123 billion versus $50
billion over ten years. But the Palestinians would gain more proportionately, with
average per capita income increasing by approximately 36 percent over what it
would have been in 2024, versus 5 percent for the average Israeli. A return to
violence would have profoundly negative economic consequences for both Palestinians and Israelis; per capita gross domestic product would fall by 46
percent in the West Bank and Gaza and by 10 percent in Israel by 2024. In most
scenarios, the value of economic opportunities gained or lost by both parties is
much larger than expected changes in direct costs. Unilateral withdrawal by Israel
from the West Bank would impose large economic costs on Israelis unless the
international community shoulders a substantial portion of the costs of relocating
settlers. Intangible factors, such as each party's security and sovereignty
aspirations, are critical considerations in understanding and resolving the impasse.
Taking advantage of the economic opportunities of a two-state solution would
require substantial investments from the public and private sectors of the
international community and from both parties.

9. What was the approximate gross domestic production (in RS.) in year 2004? (1$ =
73.25 INR)
(a) 877078.50 (b) 988142.5 (c) 978650.25 (d) 967892.5
10.The total population of the Palestinian Territory increased by 20% over a decade
from 2004, out of which 75% of the people lived in Gaza. Also, if 60% of Gaza’s
population is considered to be young then the total number of persons who are not
young but are still unemployed are: (Consider all the people who live outside Gaza
as employed)
(a) 65000
(b) 64000
(c) 64800
(d) None of these

Consider the following results for two samples randomly taken from two populations.

Sample A Sample B

Sample Size 31 35

Sample Mean 106 102

Sample Standard Deviation 8 7

Test the hypothesis Ho=sigma1-sigma2=0 vs Ha=sigma1-sigma2 do not equal 0 at 5% level of significance. Show all six steps using p-value approach.

The market and Stock J have the following probability distributions:

a. Calculate the expected rate of return for the market. Round your answer to two decimal places.

a1. Calculate the expected rate of return for Stock J. Round your answer to two decimal place

b. Calculate the standard deviation for the market. Do not round intermediate calculations. Round your answer to two decimal places.

b2. Calculate the standard deviation for Stock J. Do not round intermediate calculations. Round your answer to two decimal places

Write this code in python Debugging:

Use the Debugging Coin Toss code below as the basis for this project. Get the program running exactly as it appears in the text. It will run as written. Although it runs, does it run (behave) correctly? That is where you will focus your debugging efforts.

Code:

import random

guess = ' '

while guess not in ('heads', 'tails'):

     print('Guess the coin toss! Enter heads or tails: ')

     guess = input()

toss = random.randint(0, 1) # 0 is tails, 1 is heads

if toss == guess:

    print('You got it!')

else:

    print('Nope! Guess again!')

    guess = input()

    if toss == guess:

        print('You got it!')

   else:

        print('Nope. You are really bad at this game.')

Tasks Your program is to accomplish the following:

1. Welcome the user to the program

2. Keep the program flow of the original text. You will probably add to the original text, but totally rewriting the code is neither required nor desired.

3. Use debugging tools to identify if/where there is an issue with the program

4. Required: Enable logging and place logging messages in your source code. See text examples for purpose and placement of logging messages.

At a minimum, have start and end program logging messages and logging messages when variable values are changed/updated.

Write the log messages to a file ‘coin_toss_log.txt’. Log messages should not go to the screen.

5. Required: Use assertions in your source code. At a minimum, place two assertions in your code.

I recommend placing assertions to do ‘sanity’ checks on variable (guess and toss) values and types.

6. Required: Leave all your debugging code in your source code. If I don’t see it, you didn’t do it.  

7. Recommended. Run your coin_toss program with IDLE’s debugger enabled. Watch the variables closely; value and type.

8. Optional. Use other tools addressed in our text. Experiment, explore, play.  

Notes - Study the code and determine what debugging tools you can use, and where to use them, to help you determine if this program is running correctly, and if not, how to correct it. - Work on your screen output. Put effort towards an attractive output that a user/gamer would find appealing. -

Design an isolated footing with one side limited to 7 ft for the following: 1 ft x 1 ft edge column, axial loads PD = 130 kip and PL = 155 kip, fc’ = 3,000 psi, fy = 60,000 psi, qa = 4 ksf, and a distance from top of backfill to bottom of footing is 4 ft. Assume the soil density is 100 pcf. For the column, fc’ = 5,000 psi. Sketch your design.

Solve in excel please, thank you

It gives the data on the lifetime in hours of a sample of 100 lightbulbs. The

company manufacturing these bulbs wants to know whether it can claim that its lightbulbs typically

last more than 1000 burning hours. So it did a study.

a. Identify the null and the alternate hypotheses for this study.

b. Can this lightbulb manufacturer claim at a significance level of 5% that its lightbulbs typically

last more than 1000 hours? What about at 1%? Test your hypothesis using both, the critical

value approach and the p-value approach. Clearly state your conclusions.

c. Under what situation would a Type-I error occur? What would be the consequences of a

Type-I error?

d. Under what situation would a Type-II error occur? What would be the consequences of a

Type-II error?

Lightbulb Lifetime

1 840.08

2 960.00

3 953.38

4 981.14

5 938.66

6 1051.14

7 907.84

8 1000.10

9 1073.20

10 1150.66

11 1010.57

12 791.59

13 896.24

14 955.35

15 937.94

16 1113.18

17 1108.81

18 773.62

19 1038.43

20 1126.55

21 950.23

22 1038.19

23 1136.67

24 1031.55

25 1074.28

26 976.90

27 1046.30

28 986.54

29 1014.83

30 920.73

31 1083.41

32 873.59

33 902.92

34 1049.17

35 998.58

36 1010.89

37 1028.71

38 1049.92

39 1080.95

40 1026.41

41 958.95

42 985.17

43 988.49

44 1012.99

45 1070.82

46 1063.13

47 948.57

48 1156.42

49 973.79

50 845.85

51 1025.35

52 931.60

53 931.69

54 1063.00

55 971.95

56 689.52

57 999.63

58 966.65

59 1022.77

60 1041.44

61 987.74

62 887.28

63 975.27

64 904.52

65 937.41

66 964.32

67 1047.56

68 1109.78

69 1053.21

70 1091.02

71 1114.46

72 967.33

73 1131.02

74 920.96

75 983.79

76 972.49

77 1001.50

78 811.08

79 1035.06

80 1001.30

81 970.45

82 1111.68

83 955.20

84 920.79

85 941.75

86 937.89

87 1024.13

88 952.33

89 879.74

90 866.77

91 1080.00

92 1002.06

93 1038.74

94 1017.37

95 988.42

96 893.74

97 1022.92

98 1081.83

99 1154.07

100 827.85

1. Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Life expectancy is a statistical measure of average time a person is expected to live, based on a number of demographic factors. Mathematically, life expectancy is the mean number of years of life remaining at a given age, assuming age-specific mortality rates remain at their most recently measured levels. Last year the average life expectancy of all the Life Insurance policyholders in Ontario at age 65 was 22.3 years (meaning that a person reaching 65 last year was expected to live, on average, until 87.3). The insurance company wants to determine if their clients now have a longer average life expectancy, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample data is provided in the excel file. Answer the following questions. Results should be support by excel output.

a. Construct a 95% and 99% confidence intervals for the true average life expectancy. Use t-distribution and Descriptive Statistics function from Data Analysis. Interpret each Confidence interval and comment on the difference between the 95% and 99% interval.

b. Write the null and alternative hypotheses for this test:

c. In this context, describe a Type I error possible. How might such an error impact Life Insurance company’s decision regarding the premium structure?

d. What is the value of the t-test statistic?

e. What is the associated P-value?

f. State the conclusion using α = 0.05. Do it using both P-value and critical value.