Assignment 13

You should type answers to the questions below (except where noted otherwise), as well as paste tables/graphs/charts, in one MS Word document, which has the name:
ma103Assignment12YOURNAME. Saving in MS Word should automatically give this file the proper extension of .doc or .docx. You should upload this file in Moodle prior to the deadline. Clearly label which Activity and problem you are answering. It might be helpful to put in a "Page Break" between the answers for different Activities, where appropriate.

When you are asked below to create a graph or a table in Excel, you may simply paste the graph or table into your Word document. You do NOT need to import the entire worksheet associated with it.

Note that the data used in the Activities is newer than the data provided in the textbook or the Excel instructions provided.

Monday, Novebmer 16

A. Read Topic 19 in the textbook, and work the assigned Exploration problems as listed for each day on the course web-site. You do NOT need to turn in the Exploration problems, but they are useful in preparing for the written exam.

B. Activity 19.1, Diagnostic Testing and Conditional Probability

Write your answers for Activity 19.1 and hand in a hard-copy. Prof. Escuadro's office is A-304, in the Brumbaugh Academic Center. You may slide it under his door if he's not in the office.

Friday, November 20

C. Read Topic 20 in the textbook, and work the assigned Exploration problems as listed for each day on the course web-site. You do NOT need to turn in the Exploration problems, but they are useful in preparing for the written exam.

D. Activity 20.1, Sampling and Surveys
In this activity, you will investigate why random sampling is important and also consider some issues involved in the design of surveys.

1. Here is a list of the 50 United States.

1. a. Using your sense of the land area of each state, choose what you think is a representative (that is, your subjective) sample of six states. Your goal is to pick a sample of six states whose mean land area is close to the mean land area of all 50 states.(It might help to try to visualize a map of the U.S. to get your sample of six "representative" states.)

Copy and paste this table into your MS Word document. It should be filled with the six states you choose. AFTER you choose the states, you should look up the land area of each state, in square miles, and enter it in the table too. You may use the Information Please Almanac for the land area.

1. b. Compute the sample mean for the land are of your subjective sample of six states, and enter it into your MS Word document. In addition, WRITE THIS NUMBER ON THE BOARD AND EMAIL IT TO YOUR INSTRUCTOR.

The following is a list of sample means (subjective, of land area) from each of the students/teams in class: Assignment 13(data).xls.

1. c. Now use Excel's random number generator to generate six random integers between 0 and 49. Recall how you generated random integers 0, 1, 2, and 3 in Activity 18.1 (= INT( 4 * RAND( ) ) )and adapt that technique to generate integers between 0 and 49. It is possible that you might get repeated numbers when you generate the random integers. If you do, discard the second occurrence of the repeated number and generate another integer so you have six distinct integers. Enter these into your MS Word document, and briefly explain the process you used to generate them.

1. d. Number the states in a systematic way, and use the numbers you generated in #1.c. of this question to pick a random sample of six states. Explain your systematic method for numbering the states.

1. e. Copy and paste the table below into your MS Word document. It should be filled with the six states you randomly chose, and their land area, in square miles. Once again, you may use the Information Please Almanac for the land area data.

1. f. Compute the sample mean for the land are of your random sample of six states, and enter it into your MS Word document. In addition, WRITE THIS NUMBER ON THE BOARD AND EMAIL IT TO YOUR INSTRUCTOR.

The following is a list of sample means (random, of land area) from each of the students/teams in class: Assignment 13(data).xls.

1. g. Recall that a population refers to the whole group about which you want to draw a conclusion and a sample refers to a subgroup of the population. The population mean land are for the population of all 50 states is approximately 70,748 square miles.

In your MS Word document, enter the number of students/teams with subjective sample means (in #1. b.) greater than the population mean of 70,748. Also, enter the number of students/teams with subjective sample means (in #1. b.) less than the population mean of 70,748.

1. h. In your MS Word document, enter the number of students/teams with random sample means (in #1. f.) greater than the population mean of 70,748. Also, enter the number of students/teams with random sample means (in #1. f.) less than the population mean of 70,748.

1. i. Explain how the class results using the two sampling methods (subjective and random) were different, if they were, or how they were similar. Were the class results unexpected?

2. Use Excel to generate a stratified random sample of six states, stratified by location ("East of" or "West of") relative to the Mississippi River.

From Topic 20, Exploration #9, here is a list of states that are east of the Mississippi River:
Alabama, Connecticut, Delaware, Florida, Georgia, Illinois, Indiana, Kentucky, Maine, Maryland, Massachusetts, Michigan, Mississippi, New Hampshire, New Jersey, New York, North Carolina, Ohio, Pennsylvania, Rhode Island, South Carolina, Tennessee, Vermont, Virginia, West Virginia, Wisconsin.

Since this is a stratified sample, you will first need to determine the size of each strata. In particular you'll need to count the number of states east of the Mississippi, and the number of states west of the Mississippi. Then, the proportion of states east of the Mississippi in your sample size of six should be the same proportion as the total number of states east of the Mississippi. Also, be sure to choose the proper number of states from each strata (East and West), you won't be able to use the state numbering used above in #1. d.

Briefly describe how you generated your stratified random sample.

2. a. Copy and paste the table below into your MS Word document. It should be filled with the six states of your stratified random sample, and their water area, in square miles. Once again, you may use the Information Please Almanac for the water area data.

2. b. Compute the sample mean water area for your stratified random sample of six states and record it in your MS Word document.

2. c. Describe how your sample mean water area compares to the population mean water area of approximately 5,133 square miles.

2. d. Explain why stratifiying a sample, as we just did in #2, is useful.

Summary
In this activity, you investigated why you would want to collect random samples rather than "subjective" samples. You also collected a stratified randome sample. To collect these random samples, you used Excel's random number generator.