The following table shows historical end-of-week adjusted close prices (including dividends) for a stock and the S&P 500.
| A | B | C | |
| 1 | Week | Stock | S&P 500 |
| 2 | 0 | 39.53 | 2,758 |
| 3 | 1 | 40.17 | 2,700 |
| 4 | 2 | 43.1 | 2,742 |
| 5 | 3 | 42.47 | 2,783 |
| 6 | 4 | 39.77 | 2,836 |
| 7 | 5 | 42.07 | 2,762 |
| 8 | 6 | 43.84 | 2,829 |
| 9 | 7 | 39.77 | 2,768 |
| 10 | 8 | 40.1 | 2,866 |
| 11 | 9 | 40.98 | 3,019 |
| 12 | 10 | 42.15 | 2,982 |
2. What is the geometric average weekly return for the S&P 500?
3. What is the annualized return for the S&P 500 (EAR)?
4. Calculate the weekly returns. What is standard deviation of weekly returns for the S&P 500?
5. What is the beta of the stock?
In: Finance
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.
| 4 | 8 | 9 | 10 | 1 | 1 | 1 | 8 | 8 | 8 | 8 | 7 | 6 |
| 7 | 8 | 8 | 10 | 9 | 1 | 8 | 7 | 8 | 7 | 9 | 8 | 10 |
| 6 | 4 | 8 | 1 | 1 | 8 | 8 | 7 | 10 | 9 | 7 | 1 | 7 |
| 5 | 8 | 4 | 1 | 9 | 8 | 9 | 1 | 1 | 7 | 7 |
Develop a 95% confidence interval estimate of the population mean rating for Miami (to 2 decimals).
( , )
In: Math
The American Housing Survey reported the following data on the number of times that owner-occupied and renter-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months. Number of Houses (1000s) Number of Times Owner Occupied Renter Occupied 0 547 23 1 5,012 541 2 6,110 3,734 3 2,544 8,660 4 times or more 557 3,784 Do not round intermediate calculations. Round your answers to two decimal places. a. Define a random variable x = number of times that owner-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months and develop a probability distribution for the random variable. (Let x = 4 represent 4 or more times.) x f(x) 0 .96 1 .9 2 .62 3 .23 4 .13 Total 2.84 b. Compute the expected value and variance for x. Total E(x) Var(x) c. Define a random variable y = number of times that renter-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months and develop a probability distribution for the random variable. (Let y = 4 represent 4 or more times.) y f(y) 0 1 2 3 4 Total d. Compute the expected value and variance for y. Total E(y) Var(y)
In: Statistics and Probability
Match each sequence to a good candidate for a closed form. Note that for each of the given sequences, the initial value of the index n is given.
| selectABCDE | 1.
f(n)=5n−2 |
| selectABCDE | 2.
f(n)=((1+5√)2)n−((1−5√)2)n5–√ |
| selectABCDE | 3.
f(n)=2n+1−1 |
| selectABCDE | 4.
f(n)=5n+3 |
| selectABCDE | 5.
f(n)=2n−1 |
| selectABCDE | 6.
f(n)=(n+1)2−1 |
| selectABCDE | 7.
f(n)=n2−1 |
In: Advanced Math
Consider independent random variables X1, X2, and X3 such that X1 is a random variable having mean 1 and variance 1, X2 is a random variable having mean 2 and variance 4, and X3 is a random variable having mean 3 and variance 9.
(a) Give the value of the variance of
X1 + (1/2)X2 + (1/3)X3
(b) Give the value of the correlation of Y = X1- X2 and Z = X2 + X3.
In: Statistics and Probability
Open House_Price data.
Test if there is a significant difference in house prices for houses that are less than 31 years old compared to houses that are 31 years or older. Answer the questions for Assessment. (Pick the closest answer)
1. What is the P-value?
2. What is the Statistical interpretation?
3. What is the conclusion?
DATA: Age #Bathrooms #Rooms #BedRooms #FirePlaces sellingPrice in $100000 42 1 7 4 0 4.9176 62 1 7 4 0 5.0208 40 1 6 3 0 4.5429 54 1 6 3 0 4.5573 42 1 6 3 0 5.0597 56 1 6 3 0 3.891 51 1 7 3 1 5.898 32 1 6 3 0 5.6039 32 1 6 3 0 5.8282 30 1 6 3 0 5.3003 30 1 5 2 0 6.2712 32 1 6 3 0 5.9592 32 1 6 3 0 5.6039 50 1.5 8 4 0 8.2464 17 1.5 6 3 0 7.7841 23 1 7 3 0 9.0384 22 1.5 6 3 0 7.5422 44 1.5 6 3 0 6.0931 3 1 7 3 0 8.14 31 1.5 8 4 0 9.1416 42 2.5 10 5 1 16.4202 14 2.5 9 5 1 14.4598 46 1 5 2 1 5.05 22 1.5 7 3 1 6.6969 40 1 6 3 1 5.9894 50 1.5 8 4 1 8.7951 48 1.5 8 4 1 8.3607 30 1.5 6 3 1 12
In: Statistics and Probability
The quarterly sales data (number of book sold) for Christian book over the past three years in California follow:
Year 1 Year 2 Year 3
1. Construct a time series plot. What type of pattern exists in the data? This was not shown in the WebEx example I provided. But you can simply create this graph in Excel (Go to INSERT and look for charts under INSERT Tab). Basically you need to provide a 2-dimensional graph showing the trend of book sales over the given time period. The vertical line represents sale for Christian book, while the horizontal line represents quarter.
2. Use the following dummy variables to develop an estimated regression equation to account for any seasonal effects in the data: Quarter1=1 if the sales data point is in Quarter 1, otherwise Quarter 1=0; Quarter 2=1 if the sales data point is in Quarter 2, otherwise, Quarter 2=0; Quarter 3=1 if the sales data point is in Quarter 3, otherwise Quarter 3=0.
3. Compute the quarterly forecasts for next year.
4. Let t=1 to refer to the observation in quarter 1 of year 1; t=2 to refer to the observation in quarter 2 of year 1;,,,, and t=12 to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (2) and t, develop an estimated regression equation to account for seasonable effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for next year.
In: Statistics and Probability
Scientist warn that food shortages are an impending future issue
for humans. A potential solution is eating non-traditional foods in
the western world. An experimental psychologist knows that
westerners are uncomfortable eating food other cultures have no
trouble eating. The psychologist developed a method to help
individuals tolerate more the eating of non-ordinary food. However,
the psychologist is unsure which type(s) of foods the method will
be more effective on. The psychologist has some participants go
through the method and then asks them to eat each of the following
out of the ordinary foods: stick insects, bovine testicles, fish
eyes, and Witchetty grubs. On each occasion, participants are
measured on how many seconds it takes before they gagged while
eating the food. The data are in the table below. What can the
psychologist concluded with α = 0.01?
| stick | bovine | fish | grub |
| 7 8 6 4 8 7 9 11 |
6 4 1 2 3 4 1 5 |
1 2 3 1 4 4 6 7 |
5 4 7 8 7 6 1 0 |
a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way
ANOVA
b) Input the appropriate value(s) to make a
decision about H0.
p-value =_______________ ;
Decision: ---Select--- Reject H0 Fail to reject H0
c) Using the SPSS results,
compute the corresponding effect size(s) and indicate
magnitude(s).
η2 = ; ---Select--- na trivial
effect small effect medium effect large effect
d) Make an interpretation based on the
results.
1) At least one of the foods differed on time before gagging.
2) None of the foods differed on time before gagging.
In: Statistics and Probability
Let B = (p0, p1, p2) be the standard basis for P2 and
B = (q1, q2, q3) where:
q1 = 1 + x , q2 = x + x
2 and q3 = 2 + x + x
2
1. Show that S is a basis for P2.
2. Find the transition matrix PS→B
3. Find the transition matrix PB→S
4. Let u = 3 + 2x + 2x
2
.
Deduce the coordinate vector for u relative to S
In: Advanced Math
1. Ogier Incorporated currently has $900 million in sales, which are projected to grow by 8% in Year 1 and by 4% in Year 2. Its operating profitability (OP) is 7%, and its capital requirement (CR) is 65%. Do not round intermediate calculations. Enter your answers in millions. For example, an answer of $1 million should be entered as 1, not 1,000,000. Round your answers to two decimal places.
What are the projected sales in Years 1 and 2 (in million)?
What are the projected amounts of net operating profit after taxes (NOPAT) for Years 1 and 2 (in million)?
What are the projected amounts of total net operating capital (OpCap) for Years 1 and 2 (in million)?
What is the projected FCF for Year 2 (in million)?
In: Finance