Question Four

An academic conference held this past January consistent of 250 participants including undergraduate students, masters students, PhD students, and, professors from business faculties, engineering faculties, and nursing faculties to discuss various ways of increasing the learning desires of students. The following table gives us the breakdown of participants by levels of education and faculties.

                                                                Business               Engineering               Nursing                    Totals

Undergraduate students                     30                               15                               35                               80

Masters students                                    40                               38                               12                               90

PhD students                                             10                               12                               8                               30

Professors                                                  20                               15                               15                               50

Totals                                                        100                               80                               70                           250

1. The probability that this participant is from business is __ 100/250_____

2. The probability that this participant is a PhD student is __30/250____

3. The probability that this participant is a nursing professor is __15/50_____

4. The probability that this participant is either an undergraduate or a master’s student is _170/250_______

5. The probability that this participant is either from business or a PhD student is ________

6. The probability that this participant is a Professor knowing that he/she is in nursing is ________

7. The probability that this participant is from business knowing that he/she is a master’s student is

_____

Researcher conducts a study to decide whether support groups improve academic performance for at-risk high school students. Ten such students are randomly selected to take part in the support group for a semester, while the other 10 at-risk students serve as a control group. At the end of the semester, the improvement in GPA versus the previous semester is recorded for each student.
Support Group: 0.5, 0.8, 0.7, 0.7, -0.1, 0.2, 0.4, 0.4, 0.5, 0.4
Control Group: -0.3, 0.0, -0.1, 0.2, -0.1, -0.2, -0.2, 0.0, -0.1, 0.1

At the 10% level, use R to compare the two groups using a permutation test (with 100,000 randomly generated permutations). You need to write your hypotheses, the test statistic, the pvalue, and the decision/conclusion in the context of the problem.

R code for reference:

SupportGroup <- c(0.5, 0.8, 0.7, 0.7, -0.1, 0.2, 0.4, 0.4, 0.5, 0.4)
ControlGroup <- c(-0.3, 0.0, -0.1, 0.2, -0.1, -0.2, -0.2, 0.0, -0.1, 0.1)

mean(SupportGroup);sd(SupportGroup)
mean(ControlGroup);sd(ControlGroup)

#permutation test on difference of means
choose(20,10)#number of possible permutations
new.dat <- c(SupportGroup,ControlGroup)
obs.mean.diff <- mean(SupportGroup) - mean(ControlGroup)
nsim <- 100000
sim.mean.diff <- rep(NA,length=nsim)
for (i in 1:nsim){
grps <- sample(c(rep(1,10),rep(2,10)),replace=FALSE)
sim.mean.diff[i] <- mean(new.dat[grps==1]) - mean(new.dat[grps==2])
}

hist(sim.mean.diff);abline(v=obs.mean.diff,col="red",lty=2)
length(sim.mean.diff[sim.mean.diff<=obs.mean.diff])/nsim #estimated p-value

Step 4:

What percent of the variation in corn yield is explained by these two variables? Give your answers to 2 decimal places and do not include units in your answers.

Percent explained by the model = %

Step 5:

Using the regression equation, find a point estimate for the corn yield for 2014 Assume that the soy bean yield for that year is 42.

Point Estimate = (Give your answer to 1 decimal place.)

ID      Year    CornYield       SoyBeanYield
1       1957    48.3    23.2
2       1958    52.8    24.2
3       1959    53.1    23.5
4       1960    54.7    23.5
5       1961    62.4    25.1
6       1962    64.7    24.2
7       1963    67.9    24.4
8       1964    62.9    22.8
9       1965    74.1    24.5
10      1966    73.1    25.4
11      1967    80.1    24.5
12      1968    79.5    26.7
13      1969    85.9    27.4
14      1970    72.4    26.7
15      1971    88.1    27.5
16      1972    97      27.8
17      1973    91.3    27.8
18      1974    71.9    23.7
19      1975    86.4    28.9
20      1976    88      26.1
21      1977    90.8    30.6
22      1978    101     29.4
23      1979    109.5   32.1
24      1980    91      26.5
25      1981    108.9   30.1
26      1982    113.2   31.5
27      1983    81.1    26.2
28      1984    106.7   28.1
29      1985    118     34.1
30      1986    119.4   33.3
31      1987    119.8   33.9
32      1988    84.6    27.0
33      1989    116.3   32.3
34      1990    118.5   34.1
35      1991    108.6   34.2
36      1992    131.5   37.6
37      1993    100.7   32.6
38      1994    138.6   41.4
39      1995    113.5   35.3
40      1996    127.1   37.6
41      1997    126.7   38.9
42      1998    134.4   38.9
43      1999    133.8   36.6
44      2000    136.9   38.1
45      2001    138.2   39.6
46      2002    129.3   38.0
47      2003    142.2   33.9
48      2004    160.3   42.2
49      2005    147.9   43.1
50      2006    149.1   42.9
51      2007    150.7   41.7
52      2008    153.9   39.7
53      2009    164.7   44.0
54      2010    152.8   43.5
55      2011    147.2   41.9
56      2012    123.4   39.8
57      2013    158.8   43.3

Serial Case

1. C6-72Calculate and compare cost estimates using high-low and regression methods (Learning Objectives 4 & 5)

This case is a continuation of the Caesars Entertainment Corporation serial case that began in Chapter 1. Refer to the introductory story in Chapter 1, here for additional background. (The components of the Caesars serial case can be completed in any order.)

Caesar Entertainment Corporation’s Form 10-K contains a variety of data in addition to financial statements. Below is a list that contains Caesars’ food and beverage costs (adapted) taken from its Statements of Operations for the past 22 years. In addition, the number of hotel rooms and suites owned by Caesars at the end of each of those 22 years has been gathered from other information provided in the Form 10-Ks.

Requirements (use excel)

1. Using the high-low method, find the following cost estimates:
   1. Variable food and beverage cost per hotel room/suite
   2. Fixed food and beverage cost per hotel room/suite
2. Perform a regression analysis using Excel. Use # of hotel rooms & suites as the X and the Food and beverage costs as the Y in your regression analysis.
   1. What is the estimated variable food and beverage cost per hotel room/suite?
   2. What is the estimated fixed food and beverage cost per hotel room/suite?
   3. In your opinion, is the number of hotel rooms and suites a good predictor of Caesars’ food and beverage costs? Why or why not?

This project is assigned to give you the chance to apply the knowledge that you have acquired in statistics to our Global Society. The following data has been collected for you and you are going to look at the possible relationships and make some decisions that might impact your life based on the outcomes.

Use the following data in this project. The data represents the Total Number of Alternative-Fueled Vehicles in use in the United States (source:  US Department of Energy:  http://tonto.eia.doe.gov/aer/)

A.) Construct a scatter diagram of year (x) vs number of Alternative-fueled vehicles in US (y). Do these variables appear to have a relationship? Write 2 or 3 sentences describing the relationship or lack of a relationship. Explain your reasoning. (9 points for graph and 9 points for description of relationship or lack of relationship)

B.)

Description of the relationship of data:_____________________________________

C.) Find the correlation and regression lines for the data above.

r= _______________________ (5 points)

= _______________ x+ _______________ (5 points)

D.) Do the variables have significant correlation? For full credit, you must show each step of the hypothesis test. Use the 0.05 significance.  (18 points total)

E.) In 2008, the price of gas dropped drastically and hit a low average of $1.59 for the nation.  What effect do you think this will have on the alternative-fuel car sales, if any?  Do you think that this would affect the number of alternative-fueled vehicles used in the United States? Do you think that it would follow the same pattern as before 2008? Write 2 or 3 sentences explaining how you think the new vehicles will affect the number of alternative-fueled vehicles in the United States. (18 points)

F.) Use your regression equation to predict the number of alternative-fueled vehicles used in the United States in 2010. Assume that the pattern remains the same after the introduction of the electric-gas vehicles. Show your work. (18 points)

G.) Search online to find some evidence for or against your opinion in part e. Give the information that you found and state the URL to the data. Was your prediction correct or incorrect? Why do you think that happened? Write 2 or 3 sentences summarizing the information that you found and explain why you think that happened. Be sure to answer each question. (18 points)

This project is assigned to give you the chance to apply the knowledge that you have acquired in statistics to our Global Society. The following data has been collected for you and you are going to look at the possible relationships and make some decisions that might impact your life based on the outcomes.

Use the following data in this project. The data represents the Total Number of Alternative-Fueled Vehicles in use in the United States (source:  US Department of Energy:  http://tonto.eia.doe.gov/aer/)

A.) Construct a scatter diagram of year (x) vs number of Alternative-fueled vehicles in US (y). Do these variables appear to have a relationship? Write 2 or 3 sentences describing the relationship or lack of a relationship. Explain your reasoning. (9 points for graph and 9 points for description of relationship or lack of relationship)

B.)

Description of the relationship of data:_____________________________________

C.) Find the correlation and regression lines for the data above.

r= _______________________ (5 points)

= _______________ x+ _______________ (5 points)

D.) Do the variables have significant correlation? For full credit, you must show each step of the hypothesis test. Use the 0.05 significance.  (18 points total)

E.) In 2008, the price of gas dropped drastically and hit a low average of $1.59 for the nation.  What effect do you think this will have on the alternative-fuel car sales, if any?  Do you think that this would affect the number of alternative-fueled vehicles used in the United States? Do you think that it would follow the same pattern as before 2008? Write 2 or 3 sentences explaining how you think the new vehicles will affect the number of alternative-fueled vehicles in the United States. (18 points)

F.) Use your regression equation to predict the number of alternative-fueled vehicles used in the United States in 2010. Assume that the pattern remains the same after the introduction of the electric-gas vehicles. Show your work. (18 points)

G.) Search online to find some evidence for or against your opinion in part e. Give the information that you found and state the URL to the data. Was your prediction correct or incorrect? Why do you think that happened? Write 2 or 3 sentences summarizing the information that you found and explain why you think that happened. Be sure to answer each question. (18 points)

You have recently been hired as a cost accountant at Travenol Laboratories. The controller is an "old school" accountant and has heard that you recently graduated with a degree in accounting. One day he summons you to his office to assign you a task. He says, "I understand that recently educated accountants are using a variety of statistical tools to determine causality between costs and their respective drivers. We have been using direct labor hours as our cost driver for our manufacturing overhead costs for as long as I have been here. In the last few years our production processes have become more automated and I am not sure whether direct labor hours is the appropriate allocation basis for our manufacturing overhead costs. I would like you to use some of those statistical tools to determine whether there is a more appropriate cost driver."

You leave his office recognizing that this is a tremendous career opportunity. If you can convince your boss that you can use statistical analysis to determine the best cost driver, you will have established yourself in the department as a knowledgeable professional. It is good fortune that one of your projects in your cost class dealt specifically with this type of analysis.

Requirement:

Calculate openness as a percentage for Paraguay and Poland. Explain how you calculated openness, i.e., write down the formula. Using a graph of Openness (as a percentage) versus time, explain in up to 200 words how openness has changed for these countries from 2001 to 2014. Put Paraguay and Poland in the same graph and make sure your graph is properly labelled.

Explain in up to 200 words the relationship between Openness and economic development by calculating the correlation coefficient between GDP per capita (proxy for economic development) and Openness for Paraguay and Poland, respectively. [Here you have to use the CORREL command in Excel].