Assignment Details

In Unit 2, you have learned about three different types of distributions: Normal, binomial, and Poisson. You can take data that you collect and plot it out onto graphs to see a visual representation of the data. By simply looking at data on a graph, you can tell a lot about how related your observed data are and if they fit into a normal distribution.

For this submission, you will be given a series of scenarios and small collections of data. You should plot the data or calculate probabilities using excel. Then, you will create your own real or hypothetical scenario to graph and explain.

Answer the following:

• The mean temperature for the month of July in Boston, Massachusetts is 73 degrees Fahrenheit. Plot the following data, which represent the observed mean temperature in Boston over the last 20 years:

  1998	72
  1999	69
  2000	78
  2001	70
  2002	67
  2003	74
  2004	73
  2005	65
  2006	77
  2007	71
  2008	75
  2009	68
  2010	72
  2011	77
  2012	65
  2013	79
  2014	77
  2015	78
  2016	72
  2017	74

  1. Is this a normal distribution? Explain your reasoning.
  2. What is an outlier? Are there any outliers in this distribution? Explain your reasoning fully.
  3. Using the above data, what is the probability that the mean will be over 76 in any given July?
  4. Using the above data, what is the probability that the mean will be over 80 in any given July?
     
• A heatwave is defined as 3 or more days in a row with a high temperature over 90 degrees Fahrenheit. Given the following high temperatures recorded over a period of 20 days, what is the probability that there will be a heatwave in the next 10 days?

  Day 1	93
  Day 2	88
  Day 3	91
  Day 4	86
  Day 5	92
  Day 6	91
  Day 7	90
  Day 8	88
  Day 9	85
  Day 10	91
  Day 11	84
  Day 12	86
  Day 13	85
  Day 14	90
  Day 15	92
  Day 16	89
  Day 17	88
  Day 18	90
  Day 19	88
  Day 20	90

Customer surveys reveal that 40% of customers purchase products online versus in the physical store location. Suppose that this business makes 12 sales in a given day

1. Does this situation fit the parameters for a binomial distribution? Explain why or why not?
2. Find the probability of the 12 sales on a given day exactly 4 are made online
3. Find the probability of the 12 sales fewer than 6 are made online
4. Find the probability of the 12 sales more than 8 are made online

Your own example:

• Choose a company that you have recently seen in the news because it is having some sort of problem or scandal, and complete the following:
  • Discuss the situation, and describe how the company could use distributions and probability statistics to learn more about how the scandal could affect its business.
  • If you were a business analyst for the company, what research would you want to do, and what kind of data would you want to collect to create a distribution?
  • Would this be a standard, binomial, or Poisson distribution? Why?
  • List and discuss at least 3 questions that you would want to create probabilities for (e.g., What is the chance that the company loses 10% of its customers in the next year?).
  • What would you hope to learn from calculating the

A government researcher is analyzing the relationship between retail sales (in $ millions) and the gross national product (GNP in $ billions). He also wonders whether there are significant differences in retail sales related to the quarters of the year. He collects 10 years of quarterly data. A portion is shown in the accompanying table. Retail sales (in millions) GNP (in billions) d1 d2 d3 2000 1 696048 9740.5 1 0 0 2 753211 9983.5 0 1 0 3 746875 10048.0 0 0 1 4 792622 10184.9 0 0 0 2001 1 704757 10206.2 1 0 0 2 779011 10350.9 0 1 0 3 756128 10332.2 0 0 1 4 827829 10463.1 0 0 0 2002 1 717302 10549.7 1 0 0 2 790486 10634.7 0 1 0 3 792657 10749.1 0 0 1 4 833877 10832.2 0 0 0 2003 1 741233 10940.2 1 0 0 2 819940 11073.6 0 1 0 3 831222 11321.2 0 0 1 4 875437 11508.3 0 0 0 2004 1 795916 11707.8 1 0 0 2 871970 11864.2 0 1 0 3 873695 12047.3 0 0 1 4 938213 12216.6 0 0 0 2005 1 836952 12486.3 1 0 0 2 932713 12613.0 0 1 0 3 940880 12848.7 0 0 1 4 987085 12994.1 0 0 0 2006 1 897180 13264.0 1 0 0 2 987406 13423.3 0 1 0 3 978211 13514.8 0 0 1 4 1018775 13683.2 0 0 0 2007 1 923997 13859.8 1 0 0 2 1016136 14087.6 0 1 0 3 1002312 14302.9 0 0 1 4 1062803 14489.9 0 0 0 2008 1 953358 14520.7 1 0 0 2 1032919 14647.3 0 1 0 3 1006551 14689.2 0 0 1 4 966329 14317.2 0 0 0 2009 1 839625 14172.2 1 0 0 2 919646 14164.2 0 1 0 3 926265 14281.9 0 0 1 4 985649 14442.8 0 0 0

a. Estimate y = β0 + β1x + β2d1 + β3d2 + β4d3 where y is retail sales, x is GNP, d1 is a dummy variable that equals 1 if quarter 1 and 0 otherwise, d2 is a dummy variable that equals 1 if quarter 2 and 0 otherwise, and d3 is a dummy variable that equals 1 if quarter 3 and 0 otherwise. Here the reference category is quarter 4. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

d-1. Reformulate the model to determine, at the 5% significance level, if sales differ between quarter 2 and quarter 3. Your model must account for all quarters. Use quarter 3 as the reference category. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Is Your Car “Made in the U.S.A.”? The phrase “made in the U.S.A.” has become a familiar battle cry as U.S. workers try to protect their jobs from overseas competition. For the past few decades, a ma- jor trade imbalance in the United States has been caused by a flood of imported goods that enter the country and are sold at lower cost than comparable American-made goods. One prime concern is the automotive industry, in which the number of imported cars steadily increased during the 1970s and 1980s. The U.S. automobile industry has been besieged with complaints about product quality, worker layoffs, and high prices, and has spent billions in advertising and research to produce an American-made car that will satisfy consumer demands. Have they been successful in stopping the flood of imported cars purchased by American consumers? The data in the table represent the numbers of imported cars y sold in the United States (in millions) for the years 1969–2009. To simplify the analysis, we have coded the year using the coded variable x = Year - 1969.

1. Using a scatterplot, plot the data for the years 1969–1988. Does there appear to be a linear relationship between the number of imported cars and the year?

2. Use a computer software package to find the least-squares line for predicting the number of imported cars as a function of year for the years 1969–1988.

3. Is there a significant linear relationship between the number of imported cars and the year?

4. Use the computer program to predict the number of cars that will be imported us- ing 95% prediction intervals for each of the years 2007, 2008, and 2009.

5. Now look at the actual data points for the years 2007–2009. Do the predictions obtained in step 4 provide accurate estimates of the actual values observed in these years? Explain.

6. Add the data for 1989–2009 to your database, and recalculate the regression line. What effect have the new data points had on the slope? What is the effect on SSE?

7. Given the form of the scatterplot for the years 1969–2009, does it appear that a straight line provides an accurate model for the data? What other type of model might be more appropriate? (Use residual plots to help answer this question.)

Calculating the Inflation Rate

Using the simple percent change formula above and the annual CPIs in the table below, it becomes possible to calculate the inflation rate between any two years.

For example, the inflation rate from 1990 to 1991 was 4.2 percent:

CPI (1991) − CPI (1990) X100

            CPI(1990)

=   136.2 – 130.7 X 100

            130.7

= 5.5/130.7 × 100

= 0.420 × 100

= 4.2%

Use the annual CPI data in the Table below to complete the inflation rate calculations for each year in Table A.

Table A: Calculating Inflation Rates

1. If you earned $10 an hour in 1994, how much would you have to earn in 1995 for your wage to have the same purchasing power?

2. If you saved $100 in 2018, how much interest would you have to earn in order for the savings to have the same purchasing power in 2019?

Table: Annual Average CPI (1982–1984 to 2012)

*Average CPI for 1982, 1983, and 1984; base level = 100.

How Much Did Things Cost in the “Good Old Days”?

Have you ever heard your parents or grandparents say, “Back in my day, a loaf of bread only cost a nickel and a gallon of gas only cost a quarter”? How can it be that things were so much cheaper back then? Were they really cheaper? You will try to answer this question by comparing modern prices to historical prices and calculating the percent increase in prices. To do so, you will examine prices of two goods: movie tickets and a McDonald’s Big Mac®.

Calculating Percent Change in Price

Percent change in price is calculated by dividing the amount of change in price by the original price and multiplying the result by 100. If the price has increased, percent change will be positive, and if the price has decreased, the percent change will be negative. The formula for calculating percent change in price:

New price – Old price × 100       OR        Price (Year 2) – Price (Year 1) × 100

Old price                                               Price (Year 1)

Historic Prices

1. Which item had the largest percent increase in price?

2. Prices seem so low in 1967. Were people much better off then? What else would

you need to know to draw a conclusion?

PC Connection and CDW are two online retailers that compete in an Internet market for digital cameras. While the products they sell are similar, the firms attempt to differentiate themselves through their service policies. Over the last couple of months, PC Connection has matched CDW’s price cuts, but has not matched its price increases. Suppose that when PC Connection matches CDW’s price changes, the inverse demand curve for CDW’s cameras is given by P = 1,200 - 2Q. When it does not match price changes, CDW’s inverse demand curve is P = 900 -0.5Q. Based on this information, determine CDW’s inverse demand function over the last couple of months.

P = ____- ____ Q if Q ≤ 200

      ____- ____ Q if Q ≥ 200

Over what range will changes in marginal cost have no effect on CDW’s profit-maximizing level of output?

$ _____to $ _______

Jeremy worked at a bank with a monthly salary of $1,500. He decided to quit his job and open a bookstore in his neighborhood. He now pays $500 in rent, $80 in utilities, and $120 in wages every month.
a.   Suppose Jeremy sells 100 books at the price of $30 every month.
i.   What is the monthly total revenue of Jeremy’s bookstore?
ii.   How much accounting profit does Jeremy make every month?
iii.   How much economic profit does Jeremy make every month?
b.   If Jeremy had not quit his job at the bank, he could have been promoted and got a pay raise of 30 percent.
i.   Will there be any changes in the monthly explicit and implicit costs of Jeremy’s bookstore?
ii.   Will there be any changes in the accounting profits of Jeremy’s bookstore?
iii.   Will there be any changes in the economic profits of Jeremy’s bookstore?

Review the tobacco -related milestones, notice the relationships between events such as advocacy groups activities, tobacco industry tactics, research reports, national policy, legislation, regulations, judicial and media advocacy. Notice changes in tobacco consumption in the United States and their relationship to the milestones in RWJFs project.

In your primary post, respond to the following, using complete sentences

Why might this report have “turned the tide” of smoking?

What effect might this report have had on policy makers?

b) Identify two additional changes (one policy & one communication- related) that impacted tobacco consumption and for each, describe the effect you saw, and describe why you think it had that effect.

What populations do you think these changes impacted most significantly and why? You may include personal story or reflection to support your case.

Suppose the demand and supply curves are described by MC = 2.76 + 1.65Q WTP = 6.45 - 0.78Q

a. Suppose the price of a substitute decreases such that WTP changes by 1.5. Note this change in WTP may be positive or negative. What is the change in quantity demanded if the market price is 4.36?

(indicate the sign of the change here) + -

(Enter only a positive number here)

b. Suppose the price of a complement decreases such that WTP changes by 1.8. Note this change in WTP may be positive or negative. What is the change in quantity demanded if the market price is 4.36?

(indicate the sign of the change here) + -

(Enter only a positive number here)

c. Suppose income decreases and the good is inferior such that WTP changes by 1.7. Note this change in WTP may be positive or negative. What is the change in quantity demanded if the market price is 4.36?

(indicate the sign of the change here) + -

(Enter only a positive number here)

PC Connection and CDW are two online retailers that compete in an Internet market for digital cameras. While the products they sell are similar, the firms attempt to differentiate themselves through their service policies. Over the last couple of months, PC Connection has matched CDW’s price cuts, but has not matched its price increases. Suppose that when PC Connection matches CDW’s price changes, the inverse demand curve for CDW’s cameras is given by P = 1,000 - 2Q. When it does not match price changes, CDW’s inverse demand curve is P = 700 -0.5Q. Based on this information, determine CDW’s inverse demand function over the last couple of months.

P =______ - ________ Q if Q ≤ 200
    

      ______ - _______ Q if Q ≥ 200

Over what range will changes in marginal cost have no effect on CDW’s profit-maximizing level of output?

$ _________ to $__________

Alan Tan is the CEO for an airline company. The company has a large proportion of its aircraft leased from manufacturers under lease agreements that can be cancelled at any time with minimal penalties. At the end of the period starting on 1 January 2019, looking at the statement of financial position prepared by the company accountant, Joyce Maine, Alan noticed a large increase in the total assets and liabilities. Not being aware of any major restructuring activities or investments during the period but having heard about a change in the accounting rules governing leases, Alan asks Joyce to prepare a report describing how the changes in those accounting rules affect the company.

Required

Joyce approaches you, a junior accountant, to summarise the changes in the treatment of some leases that caused the large increase in the total assets and liabilities. Provide a short description of those changes to Joyce.