Problem # 1

The monthly sales for Telco Batteries Inc. were as follows:

                        Sales

Month            (000 units)

January            20

February          21

March              15

April                14

May                 13

June                 16

July                 17

August            18

September       20

October           20

November       21

December        23

1. Plot the monthly sales data.
2. Forecast coming January sales using each of the following:
   1. The naïve approach
   2. A 6-month moving average
   3. A 6-month weighted average using 0.1, 0.1, 0.1, 0.2, 0.2 and 0.3, with the heaviest weights applied to the most recent months.
3. Calculate the mean absolute deviation (MAD) and the mean squared error (MSE) for each of the method above. Which is better among the three methods?

Allele frequency is the relative frequency of a certain allele type among a certain population. Suppose that within a certain area, the allele frequency of A, B and O are 0.2, 0.1, and 0.7, respectively. Suppose that when randomly picking up a person, the first allele type is independent of the second allele type regardless of the type. Calculate the following probabilities:

• The probability for this person to have type O blood.

• The probability for this person to have type A blood.

• The probability for this person to have type B blood.

• The probability for this person to have type AB blood.

Consider the following scenario analysis:

Assume a portfolio with weights of 0.60 in stocks and 0.40 in bonds.

a. What is the rate of return on the portfolio in each scenario? (Enter your answer as a percent rounded to 1 decimal place.)

b. What are the expected rate of return and standard deviation of the portfolio? (Enter your answer as a percent rounded to 2 decimal places.)

Assume these were the inflation rates and U.S. stock market and Treasury bill returns between 1929 and 1933:

1. What was the real return on the stock market in each year?

2. What was the average real return?

3. What was the risk premium in each year?

4. What was the average risk premium?

Following are the number of victories for the Blue Sox and the hotel occupancy rate for the past eight years. You have been asked to test three forecasting methods to see which method provides a better forecast for the Number of Blue Sox Wins.

For the following, you are to provide all forecasts to one decimal place (example, 93.2)

You are asked to forecast the Number of Blue Sox Wins for Year 9. Although you believe there might be a linear regression relationship, your boss has told you to only consider the following three forecasting methods:

• 3-period moving average
• 3-period weighted moving average given the weights of 0.7 for the most recent period and 0.2 for the next most recent period, and the remaining weight (s) consistent with this method as we have used in class, and
• exponential smoothing with α = 0.25 and the best forecast available for the Number of Blue Sox Wins is for Year 2 which is 66.0.

a) What is the forecast from each of these methods for Year 9?

b) Which forecasting method provides the better forecast for Year 9? Why? Your selection criteria must be based on one of the numerical evaluation methods we have used on the homework this term using the forecast results for Year 5 through Year 8.

Use the following information for the next 7 problems:

A simple random sample of 40 recorded speeds is obtained from cars traveling on a section of interstate 405 in Los Angeles. The sample has a mean of 68.4 miles per hour and a standard deviation of 5.7 miles per hour.

We wish to test the hypothesis that the mean speed of cars on this stretch of road is higher than the posted speed limit of 65 miles per hour. Test at a 0.5 level.

Question 15: What do yoy need to write down for the DATA SUMMARY of this problem?

A. sample size, number of successes, sample proportion

B. Sample size, sample mean, standard deviation

C. sample size, sample mean, population standard deviation

Question 16: Which of the following decribes the null and alternation hypothesis for this problem:

A. H0 u = 65, H1 u > 65

B. H0 u =68.4, H1 u <68.4

C. H0 u = 65, H1 u =/ 65

D. H0 u =68.4, H1 u =/ 68.4

Question 17: Which command in stat crunch do you use here?

A. z stats

B. T stats

C. Proportion stats

D. variance stat

Question 18: What is the p-value for this problem?

A. 0.05

B. 0.006

C. 0.003

D. 0.997

Question 19: do we reject the null hypothesis at the 0.05 level here?

A. Yes

B. No

Question 20: In plain english, what is the conclusion to the hypothesis test here?

A. the population mean speed is 68.4 MPH

B. The population mean speed is less than 68.4 MPH

C. The population mean speed is not 65 MPH

D. The population mean speed is faster that 65 MPH

Question 21: Calculate the 90% confidence interval estimate for the mean speed on I 405 in Los Angleles. We are 90% confident that the mean speed on I 405 is between 66.9 MPH and __________?

A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected.
(a) Develop a scatterplot with Distance to Work (miles) as the independent variable. Format the scatterplot to your preferences with the proper labels on the axes. In a textbox describe the relationship, if any, between the two variables. Add a linear trendline to the scatterplot, displaying the equation and R-squared value on the chart. [The scatterplot may be placed on this worksheet, a new worksheet or it's own sheet, as long as the chart is a respectable size for grading purposes.]
(b) On a new worksheet, labeled Calculations, create a table to calculate the estimated regression equation as the example in the text (Table 4.2) and the example done in class. Terms to calculate will be X-bar; Y-bar; (X - X-bar); (Y - Y-bar); (X - X-bar)*(Y - Y-bar); (X - X-bar)2. Calculate the slope coefficient (b1) and intercept (b0) in Excel using the table. Write the estimated regression equation.
(c) On a new worksheet, labeled Regression, provide the regression analysis using the Data Analysis addin tool. (You may wish to answer the following questions in a textbox.)
i. Write the estimated regression equation from the regression output.
ii. Interpret the coefficient for the independent variable, i.e. if X were to change, what is the result to Y.
iii. Interpret the coefficient of determination (R2) for the model.
iv. Test for the significance of the relationship at the 0.05 level of significance.
(d) Using the estimated regression equation, calculate the expected number of days absent for employees living 5 miles from the company


Distance to Work Number of Days Absent
1 8
3 5
4 8
6 7
8 6
10 3
12 5
14 2
14 4
18 2

Read the following scenario and complete each of the seven problems below:

A new car manufacturing company has emerged and has claimed that its new hybrid car, the Pusho, gets a better gas mileage than the highest ranked Toyota Prius. Consumer Reports Magazine decides to test this claim at a 5% level of significance. Consumer Reports randomly selects 10 of each type of car, calculates the miles per gallon for each car in the study, and records the data in the table below. Assume miles per gallon of the cars is normally distributed.

Pusho 54.1     52.4    55.7 49.7   50.6      48.9    51.8    54.5    56.9    49.8

Prius   53.2     54.3    49.8    50.1    50.5     56.1    47.8    53.4    56.8    48.7

A. Evaluate the claim that the Pusho gets a better gas mileage than the highest ranked Prius using the data from the Consumer Reports study.

1. Identify the type of test you will use to test this claim. Explain your reasoning. 2. State the null and alternate hypotheses. 3. Conduct the hypothesis test and determine the p-value. 4. State your conclusion about the claim. 5. Construct a 90% confidence interval for this study.

1.

2.

3.

4.

5.

Suppose that Toyota makes a counter-claim that their Prius has a higher gas mileage than Pusho. How could the alternative hypotheses from Part A be changed to test Toyota’s claim? Conduct the hypothesis test at the 5% level of significance for Toyota’s claim using the data above and determine the p-value. State your conclusion about the claim. Construct a 98% confidence interval for this study.

1.

2.

3.

4.

C. Based on your analysis of both claims from the makers of Pusho and Prius, what statement can be made about the miles per gallon of the two cars? Explain your reasoning.