The general fund budget (in billions of dollars) for a U.S. state for 1988 (period 1) to 2011 (period 24) follows.

(b)Develop a linear trend equation for this time series to forecast the budget (in billions of dollars). (Round your numerical values to three decimal places.)

T_t = ____?______

(c)What is the forecast (in billions of dollars) for period 25? (Round your answer to two decimal places.)

$___?_____ billion

An automobile insurance company divides customers into three categories, good risks, medium risks, and poor risks. Assume that 74% of the customers are good risks, 20% are medium risks, and 6% are poor risks. Assume that during the course of a year, a good risk customer has probability 0.005 of filing an accident claim, a medium risk customer has probability 0.01, and a poor risk customer has probability 0.025. A customer is chosen at random.

What is the probability that the customer is a good risk and has filed a claim? Round the answer to four decimal places.

What is the probability that the customer has filed a claim? Round the answer to four decimal places.

Given that the customer has filed a claim, what is the probability that the customer is a good risk?

For the past 104 ​years, a certain state suffered 27 direct hits from major​ (category 3 to​ 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution. Complete parts​ (a) through​ (d). a) What is the probability that the state will not be hit by any major hurricanes in a single​ year? The probability is nothing.​ (Round to four decimal places as​ needed.) ​(b) What is the probability that the state will be hit by at least one major hurricane in a single​ year? The probability is nothing. ​(Round to four decimal places as​ needed.) Is this​ unusual? Yes No ​(c) What is the probability that the state will be hit by at least three major hurricanes in a single​ year, as happened last​ year? The probability is nothing. ​(Round to four decimal places as​ needed.) Does this indicate that the 2004 hurricane season in this state was​ unusual?

6. ​Recently, fixed mortgage rates have been at historical lows due to the housing slowdown. The data table linked below shows the​ 30-year fixed average mortgage rate for the month of December every year between 1987 and 2010.

Year   Rate_(%)
1987   11.09
1988   11.04
1989   10.17
1990   9.93
1991   8.57
1992   8.3
1993   7.25
1994   9.04
1995   7.21
1996   7.06
1997   7.07
1998   6.84
1999   7.65
2000   7.74
2001   7.07
2002   6.84
2003   6.94
2004   6.79
2005   7.02
2006   6.82
2007   6.63
2008   5.88
2009   5.64
2010   5.4

b. Forecast the average December mortgage rate in 2011 using a trend projection ​(Round to two decimal places as​ needed.)

c. Calculate the MAD for this forecast. ​(Round to two decimal places as​ needed.)

d. Determine the Durbin–Watson statistic (Round to two decimal places as​ needed.)

e. Identify the critical values. ​(Round to two decimal places as​ needed.)

6. ​Recently, fixed mortgage rates have been at historical lows due to the housing slowdown. The data table linked below shows the​30-year fixed average mortgage rate for the month of December every year between 1987 and 2010.

Year   Rate_(%)
1987   11.09
1988   11.04
1989   10.17
1990   9.93
1991   8.57
1992   8.3
1993   7.25
1994   9.04
1995   7.21
1996   7.06
1997   7.07
1998   6.84
1999   7.65
2000   7.74
2001   7.07
2002   6.84
2003   6.94
2004   6.79
2005   7.02
2006   6.82
2007   6.63
2008   5.88
2009   5.64
2010   5.4

b. Forecast the average December mortgage rate in 2011 using a trend projection ​(Round to two decimal places as​ needed.)

c. Calculate the MAD for this forecast. ​(Round to two decimal places as​ needed.)

d. Determine the Durbin–Watson statistic (Round to two decimal places as​ needed.)

e. Identify the critical values. ​(Round to two decimal places as​ needed.)

The accompanying data table show the percentage of tax returns filed electronically in a city from 2000 to 2009. Complete parts a through e below.

Year   Percentage
2000   25
2001   33
2002   37
2003   38
2004   48
2005   50
2006   55
2007   59
2008   62
2009   64

a) Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with alpha= 0.1.

​b) Calculate the MAD for the forecast in part a.

c) Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment. Set alpha= 0.3 and beta= 0.4.

​d) Calculate the MAD for the forecast in part c.

The number of users of a certain website (in millions) from 2004 through 2011 follows.

Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast users (in millions). (Round your numerical values to one decimal place.)

T_t =

Consider the following time series.

b) Use the following dummy variables to develop an estimated regression equation to account for seasonal effects in the data:

x₁ = 1 if quarter 1, 0 otherwise; x₂ = 1 if quarter 2, 0 otherwise; x₃ = 1 if quarter 3, 0 otherwise.

=

(c)Compute the quarterly forecasts for next year.

quarter 1 forecast

quarter 2 forecast

quarter 3 forecast

quarter 4 forecast

1. Listed below is the selling price for a share of PepsiCO Inc. at the close of each year.

Year             Price                            Year                Price

1990             12.9135                       2000                49.5625

1991             16.8250                       2001                48.6803

1992             20.6125                       2002                42.2211

1993             20.3024                       2003                46.6215

1994             18.3160                       2004                52.2019

1995             27.7538                       2005                59.8534

1996             29.0581                       2006                62.0002

1997             36.0155                       2007                77.5108

1998             40.6111                       2008                54.7719

1999             35.0230                       2009                60.8025

a. Plot the data.

b. Use EXCEL’s Data Analysis add-in to determine the least squares trend equation.

c. Discuss the regression equation and include both the coefficient of determination and the          

   correlation coefficient in the discussion. Make sure to test the coefficient to determine if  

   it is statistically significant at the .01 significance level.

d. Calculate the points for the years 1992 and 2004.

e. (i) Estimate the selling price in 2014.                                                                                                                       

(ii) Does this seem like a reasonable estimate based on historical data? Why or why not?

f. By how much has the stock price increased or decreased (per year) on average during the period?

Show ALL of your work and show it in a neat and orderly fashion.

Question 1: Table 1 shows the number of customers visited by a salesman over an 80-week period. Table 1: Customers Visited Over an 80-Week Period 68 64 75 82 68 60 62 88 76 93 73 79 88 73 60 93 71 59 85 75 61 65 75 87 74 62 95 78 63 72 66 78 82 75 94 77 69 74 68 60 96 78 89 61 75 95 60 79 83 71 79 62 67 97 78 85 76 65 71 75 65 80 73 57 88 78 62 76 53 74 86 67 73 81 72 63 76 75 85 77

a) Determine the mean, mode(s) and median.

Question 1: Table 1 shows the number of customers visited by a salesman over an 80-week period. Table 1: Customers Visited Over an 80-Week Period 68 64 75 82 68 60 62 88 76 93 73 79 88 73 60 93 71 59 85 75 61 65 75 87 74 62 95 78 63 72 66 78 82 75 94 77 69 74 68 60 96 78 89 61 75 95 60 79 83 71 79 62 67 97 78 85 76 65 71 75 65 80 73 57 88 78 62 76 53 74 86 67 73 81 72 63 76 75 85 77

b) Determine the values for the first and third quartiles (Q1 and Q3).