Lab 2 - Elementary Applied Statistics - Fall 2005 | STAT 280, Lab Reports of Statistics

Material Type: Lab; Class: ELEMENTARY APPLIED STATISTICS; Subject: Statistics; University: Rice University; Term: Fall 2005;

Typology: Lab Reports

Pre 2010

Uploaded on 08/19/2009

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STAT 280 fall 2005
Lab 2
Lab 2 is due one week from your lab to your TA. Your TA means the TA who is
instructing the lab you have registered for. Labs my be turned in to your TA’s mailbox
located in DH 1092 or handed in to him/her in person after the lab. E-mail submissions
are not accepted.
Labs are to be written up in legible reports with all graphs labeled. It is possible to insert
graphs and spreadsheets into a Microsoft word document, but this is not necessary.
The file name of the data is DataSet2.XLS available on the courses website. This data
set is also on the CD found attached to the back cover of your textbook. On the CD this
data is called CS.XLS. In the CD Drive, click the PCDataSets folder, then the Excel
folder, then the Appendix folder, and you will see the CS.XLS file. Double-click to
open this file in Excel.
You also need to make sure the Analysis ToolPak add-in is installed on Excel. In Excel,
go to Tools Add-Ins and make sure Analysis ToolPak is checked and click Ok. For
this lab you will also need to make sure the S-Plus option is checked. The S-Plus option
is found under the Analysis ToolPak option.
Codebook [i.e. what the columns mean in the data set]
1. OBS – this is the number each student was assigned from 1 to 224.
2. GPA – the student’s GPA for their first three semesters of college (4-point scale).
3. HSM– average high school grade in math
4. HSS – average high school grade in science
5. HSE – average high school grade in English
6. SATM – SAT math score
7. SATV – SAT verbal score
8. SEX – 1 for male, 2 for female
Objective
The purpose of this lab is to help you understand the normal distribution and how to
identify normal distributions from graphs. You should also learn how to make
comparisons between sample populations using graphs. Finally we wish to look at
relationships between variables by exploring correlation.
Tasks
1. In Lab1 we calculated probabilities using excel, we will revisit that technique here.
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STAT 280 fall 2005

Lab 2

Lab 2 is due one week from your lab to your TA. Your TA means the TA who is instructing the lab you have registered for. Labs my be turned in to your TA’s mailbox located in DH 1092 or handed in to him/her in person after the lab. E-mail submissions are not accepted. Labs are to be written up in legible reports with all graphs labeled. It is possible to insert graphs and spreadsheets into a Microsoft word document, but this is not necessary. The file name of the data is DataSet2.XLS available on the courses website. This data set is also on the CD found attached to the back cover of your textbook. On the CD this data is called CS.XLS. In the CD Drive, click the PCDataSets folder, then the Excel folder, then the Appendix folder, and you will see the CS.XLS file. Double-click to open this file in Excel. You also need to make sure the Analysis ToolPak add-in is installed on Excel. In Excel, go to ToolsAdd-Ins and make sure Analysis ToolPak is checked and click Ok. For this lab you will also need to make sure the S-Plus option is checked. The S-Plus option is found under the Analysis ToolPak option. Codebook [i.e. what the columns mean in the data set]

  1. OBS – this is the number each student was assigned from 1 to 224.
  2. GPA – the student’s GPA for their first three semesters of college (4-point scale).
  3. HSM– average high school grade in math
  4. HSS – average high school grade in science
  5. HSE – average high school grade in English
  6. SATM – SAT math score
  7. SATV – SAT verbal score
  8. SEX – 1 for male, 2 for female Objective The purpose of this lab is to help you understand the normal distribution and how to identify normal distributions from graphs. You should also learn how to make comparisons between sample populations using graphs. Finally we wish to look at relationships between variables by exploring correlation. Tasks
  9. In Lab1 we calculated probabilities using excel, we will revisit that technique here.

a) Suppose Z has a Standard Normal Distribution. [Z < z] is called an Event and z is any real number. Place the events [Z < 0.05], [Z < - 4.00000789], and [Z < 1.6] in order from smallest probability to largest probability without using Excel or any tables. Explain how do you know this is the correct order for the events? b) Find the following probabilities using Excel:

  1. Z < -4.
  2. Z < 0.
  3. Z > 0.
  4. Z < 2.
  5. Z > 2. Do each of these probabilities match what you would calculate using standard normal tables from your text? If they do you know your using the Excel function correctly. How could you calculate the probabilities of b) 3. and b) 5. above without using Excel or tables? c) Suppose the random variable X has a normal distribution with mean 5 and standard deviation 8. If we were to use tables to find the probabilities of this distribution, we would first have to transform X into a standard normal random variable, Z, then find the probabilities on the standard normal tables. Excel, however, will automatically do the transformations for us. Find the following probabilities using Excel. Convince yourself these are correct by transforming X into Z and using the tables from your textbook.
  6. X < -2.
  7. X < 5.
  8. X > 5.
  9. For this problem, we are interested in comparing the SAT mathematics scores and grade point averages of female students with those of male students. Make two sets of side-by-side boxplots to carry out these comparisons. Write a brief discussion of the male-female comparisons. Does any group show outliers in either graph? If so, what group?
  10. Make normal quantile plot of grade point averages and SAT math scores for both men and women separately. Which of the four distributions are approximately normal?
  11. a) Use Excel to determine if there is strong or weak correlation between the students average high school grade in math and their average high school grade in science. Consider all the students (male and female) together for this problem. b) Use Excel to calculate the correlation coefficient between the students GPA and SAT
  1. Correlation measures the strength of a ______________ relationship between two variables. This is an idea many beginning statistics students get wrong.