Home Work Assignment 3

for MSIS 385 section 02

Last modified on 2/28/99 9:50 PM

Due March 9 1999 in class

Note:

Make sure to put your name, student ID number and the date on the handout

 

Question 1

Do problem 10.6 on page 349.

Question 2

Do problem 10.10 on page 353.

Question 3

Do problem 10.40 part a on page 362

Question 4

Do problem 10.46 on page 364.

Question 5

Do problem 10.55 on page 367.

Question 6

A sample of 10 students from among Rutgers male students were chosen at random and their heights were found to be

5'9", 6'0", 5'4", 6'1", 5'11", 4'11", 5'7", 6'3", 5'10", 5'2"

where 5'9" means five feet and nine inches. Assuming the heights are normally distributed, give a 90% confidence interval for the average height of Rutgers male students.

Question 7

Park rangers in the Yosemite national park want to estimate the total number of rain deer in the park. They pick 50 deer at random and tag their ears and then let them go. A few days later, they pick 80 rain deer at random and find out that 1/5 of them are tagged. Find an 80% confidence interval for the size of the number of rain deer in Yosemite.

Comment: This problem can be solved by trying to estimate an 80% confidence interval for the proportion of tagged deer. Then, if the true proportion is, say, p, we know that p=m/N where m the number of tagged deer is known (50 in this example) and N is the total population. Thus an approximation for p yields and approximation for N. Transform the confidence interval for p to one for N.

Question 8

Consider the following set of data

X

1

3

4

6

8

9

11

14

Y

1

2

4

4

5

7

8

9

 

  1. Fit a least square line using X as the independent variable. Show all the steps and intermediate calculations for finding the intercept and slope of the line. (You should use the formulas presented in the text or lectures to calculate these quantities, you may use Excel to verify your answer though.)
  2. Do part a) except that this time Y is assumed to be the independent variable.
  3. Draw (using Excel or by hand on a graph paper) both the scatter diagram and the two lines you obtained in parts a) and b).
  4. Assuming X is the independent variable what are the estimated values of Y for values of X=2, 5, 7?
  5. Find the standard error of estimate for the case where X is the independent variable. Repeat again for when Y is the independent variable.
  6. What are the explained and unexplained errors when X is the independent variable? Repeat when Y is the independent variable. What is the coefficient of determination r2 when X is independent? Repeat when Y is independent. Comment on the result of the last two questions.

Question 9

An Excel project. In the file Excel world.xls located at

http://rutcor.rutgers.edu/~alizadeh/CLASSES/99sprMIS385/Homeworks/world.xls

some data about economic and social activities of countries of the world are presented. This data is obtained from the Web site of world bank. The data contains per capita Gross Domestic Product (GDP) of each country along with information about other social and economic activities such as percentage of child malnutrition, life expectancy for male and female and illiteracy rate for adults, both male and female. Use Excel to download this file and answer the problems below using a separate Excel worksheet for each question. Hand in the results on a floppy disk clearly labeled with your name and ID number. In addition on the label write "Homework assignment 3 question 9". Note: It is important that you download the from within Excel. If you use Netscape and save this file and then try to load in Excel it may not work properly.

  1. Plot a scatter diagram depicting the per capita GDP as the independent variable and child malnutrition rate as dependent variable. Plot the least-squares regression line for the scatter diagram and display the line equation and the r2. Make sure to properly label the X-axis, and the Y-axis and also label the chart appropriately. Save your work in a worksheet called 9a.
  2. Now use the adult male illiteracy as the independent variable and per capita GDP as the dependent variable and follow just like part a) above. Save the result in the worksheet named 9b.
  3. Do part b but use adult female illiteracy rate as the independent variable. Save your work in a worksheet called 9c.
  4. Compare the line equations of per capita GDP versus male and female illiteracy rates. Discuss if any conclusions can be drawn from this difference. (Note this question does not have "a correct answer". I like to know how you would analyze such results.)

 


 

 

 

 

 

 

Return to: Homework page | MSIS 385 page