Your insurance company has converged for three types of cars. The annual cost for each type of cars can be modeled using Gaussian (Normal) distribution, with the following parameters: (Discussions allowed!)

• Car type 1 Mean=$520 and Standard Deviation=$110
• Car type 2 Mean=$720 and Standard Deviation=$170
• Car type 3 Mean=$470 and Standard Deviation=$80

Use Random number generator and simulate 1000 long columns, for each of the three cases. Example: for the Car type 1, use Number of variables=1, Number of random numbers=1000, Distribution=Normal, Mean=520 and Standard deviation=110, and leave random Seed empty.

Next: use either sorting to construct the appropriate histogram or rule of thumb to answer the questions:

13. What is approximate probability that Car Type 3 has annual cost less than $550?

• a. Between 1% and 3%
• b. Between 27% and 39%
• c. Between 75% and 90%
• d. None of these

14. Which of the three types of cars is most likely to cost less than $400?

• a. Type 1
• b. Type 2
• c. Type 3

15. For which of the three types we have the highest probability that it will cost between $500 and $700?

• a. Type 1
• b. Type 2
• c. Type 3

The mean salary of NBA players in 1996 was $3 million. You are interested to know if the mean salary of NBA players increased between 1996 and 2006. A simple random sample of 90 professional basketball player salaries in 2006 was recorded.

salaries from 2006

Calculate the test statistic, degrees of freedom, and P-value for a test of H0:μ=$3 million against Ha:μ>$3 million. Assume the requirements are satisfied. Input your answers below.

Which hypothesis test would be most appropriate for this study?

What is the test statistic?

What are the degrees of freedom?

What is the P-value? (Round to 3 decimal places). How do you find the p value?

Based on the results of this test, is there enough evidence to say that the mean salary of NBA players increased from 1996 to 2006? Use a level of significance of α=0.05.

The following data were obtained in a study using three separate samples to compare three different treatments. Conduct an analysis of variance with α=0.05α=0.05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments.

F-ratio =
p-value =
Conclusion:

• There is a significant difference between treatments
• These data do not provide evidence of a difference between the treatments

η2=η2=

The above data was changed by increasing the variance within each sample (note below how the data sets have changed).

Before you begin the calculation, predict how the changes in the data should influence the outcome of the analysis. That is, how will the F-ratio for these data compare with the F-ratio from above?

F-ratio =
p-value =
Conclusion:

• There is a significant difference between treatments
• These data do not provide evidence of a difference between the treatments

η2=η2=

13. Given the following data on the Dollar/Pound exchange rate (y) and the U.S. CPI (x), determine the linear regression equation, and include the Summary Output from Excel. • Based on the Summary Output is the coefficient b2 significant using the t-table (one-tail) at the 5% level with n-2 df? Prove your answer using data from the t-table. • Does the relationship given by the regression equation seem to be a reasonable economic model-- is it reasonable to assume that in this model y = f(x)? Explain why or why not. y x Period Exchange rate $ / £ CPI US 1985 1.2974 107.6 1986 1.4677 109.6 1987 1.6398 113.6 1988 1.7813 118.3 1989 1.6382 124 1990 1.7841 130.7 1991 1.7674 136.2 1992 1.7663 140.3 1993 1.5016 144.5 1994 1.5319 148.2 1995 1.5785 152.4 1996 1.5607 156.9 1997 1.6376 160.5 1998 1.6573 163 1999 1.6172 166.6 2000 1.5156 172.2 2001 1.4396 177.1 2002 1.5025 179.9 2003 1.6347 184 2004 1.833 188.9 2005 1.8204 195.3 2006 1.8434 201.6 2007 2.002 207.342

When performing calculations in the following problems, use the numbers in the table as-is. I.e., do NOT convert 8.5985 to 8.5985% (or 0.085985). Just use plain 8.5985.

1. Compute the Sortino Ratio of the portfolio using a minimal acceptable return of R M A = 3 . To calculate DDp :

1. Compute R p − R M A each year.
2. n = number of years R p − R M A < 0 .
3. DD p = square root of 1/ n− 1 ∑ ( R p − R M A )^2 for the years when R p − R M A < 0

The admissions data for freshmen at a college in the past 10 years are as follows:

1. Plot the number of applications.
2. Develop a trend model to forecast the number of applications for next year. Calculate the R² of that model and the estimated number of applications for the next year.
3. Plot the percentage of acceptances relative to the number of offers made (acceptance yield).
4. Develop a trend model to forecast next year’s acceptance yield. Calculate the R² of that model and the estimated yield for next year.
5. Assume that the college is planning for an entering class of 5,000 freshmen for each of the next two years and a class of 5,300 in the following year. What is the number of offers it should make in each year? Is it getting tougher to get into this college?

use excel AND SHOW EXCEL FORMULAS

Year # Cool Ranch Price of Cool Ranch # Nacho Cheesier Price of Nacho Cheesier 2005 10 $5 20 $5 2006 15 $4 20 $6 Suppose the nation of El Dorito produces only two products, Cool Ranch and Nacho Cheesier. The prices and quantities are shown for two years above. What was nominal GDP in 2005? It was Blank 1. Fill in the blank, read surrounding text. . What was nominal GDP in 2006? It was Blank 2. Fill in the blank, read surrounding text. . Now determine what Real GDP was in 2005 using 2006 dollars. It was Blank 3. Fill in the blank, read surrounding text. . Just for fun, figure out what Real GDP was in 2006 using 2005 as the base year. Blank 4. Fill in the blank, read surrounding text. . Now if we use 2005 for the base year again, what is the GDP deflator for 2006? Blank 5. Fill in the blank, read surrounding text. Use at least two decimal places!

Write a C# program that prints a calendar for a given year. Call this program calendar. The program prompts the user for two inputs:
      1) The year for which you are generating the calendar.
      2) The day of the week that January first is on, you will use the following notation to set the day of the week:
    
      0 Sunday                     1 Monday                   2 Tuesday                   3 Wednesday
      4 Thursday                 5 Friday                      6 Saturday

Your program should generate a calendar similar to the one shown in the example output below. The calendar should be printed on the screen. Your program should be able to handle leap years. A leap year is a year in which we have 366 days. That extra day comes at the end of February. Thus, a leap year has 366 days with 29 days in February. A century year is a leap year if it is divisible by 400. Other years divisible by 4 but not by 100 are also leap years.

Example: Year 2000 is a leap year because it is divisible by 400.  Year 2004 is a leap year because it is divisible by 4 but not by 100.
Your program should clearly describe the functionality of each function and should display the instructions on how to run the program.

Your need to create one method “displayMonth” for print each month as required. You can choose return method or not that depend on your design.

Sample Input:

Enter the year for which you wish to generate the calendar: 2004
Enter the day of the week that January first is on: 4

Sample output:

Calendar for year 2004

January
Sun      Mon     Tue      Wed     Thu      Fri        Sat
                                                1          2          3
4          5          6          7          8          9          10
11        12        13        14        15        16        17
18        19        20        21        22        23        24
25        26        27        28        29        30        31

February
Sun      Mon     Tue      Wed     Thu      Fri        Sat
1          2          3          4          5          6          7
..         ..          ..          ..          ..          ..          ..
..          ..