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STAT225 Spring 2014

Final Project

There are a possible 100 points on this final project.   The final project is worth 24% of your final grade.

The final project is due on March 30, 2014.  There will be no extensions or opportunity to revise available on this assignment.  Please make sure you have posted this work to your Assignments Folder by midnight on Sunday, March 30, 2014.

At the University of Mytholopolois the head of the statistics department wants to find out whether or not 7 basic topics are being adequately learned in introductory statistics courses.  A test is written that has 7 questions, one question addressing each of the main topics under consideration.  These topics are:

1 – measurement scales

2 – measures of central tendency

3 – standard deviation

4 – normal curve and empirical rule

5 – t-tests

6 – ANOVA

7 – correlation and regression

This brief test is going to be administered to all students registered in the introductory statistics course at the beginning of the first session and the end of the last session.  This is a pre-test/post-test design.  But before this full scale data collection effort begins the department is going to test this little instrument.   Eight students are selected to use as a test group.  The following is a table of the student scores in the pre-test condition and the post-test condition.

This final project is asking you to consider 4 different statistical tests.  The first is what the department head is looking for, the second is an extension of that with a further breakdown of information, the third is looking for a relationship between two different variables and the fourth is asking what test you would use to predict a students score.

 Student Sex Pre-test Post-test Hours per week studying statistics Matilda F 4 6 15 Franklin M 2 5 18 Lily F 4 7 13 Paul M 3 6 11 Louise F 5 5 7 Golda F 4 6 12 Duncan M 2 5 14 Philip M 6 7 9

There is a limited amount of data presented here because I don’t want to overwhelm you with long calculations.  Please assume that the distribution is normal.

Preliminary information about the data (36 points):

 Points Question 3 points 1.  What is the head of the statistics department trying to find out? 4points 2.  What are the data elements (variables) that are being collected by the researcher? 4 points 3.  What is the measurement scale of the each of the variables of interest? 2 points 4.  What is the mean of the pre-test scores? 2 points 5.  What is the median of the post-test scores? 2 points 6.  In both the pre and post test conditions, considering these as a single sample, what is the mode?  (There should be 16 values considered.) 2 points 7.  What is the range of the hours studied values? 3 points 8.  Can you calculate a mean for the sex of the students involved in this pilot study?  Explain your answer. 6 points 9.  What is the standard deviation of the pre-test scores?   Please show all your work. You don’t have to do the standard deviation of the post-test scores. 3 points 10. Looking at the pre-test is the distribution of these scores normal?  Demonstrate this with a stem and leaf plot (you’ll need to look this up on the web). 5 points 11. State the percentages of the empirical rule.

First statistical test (29 points):

Second statistical test (16 points):

In your first statistical test you tried to find out whether or not there was a difference between two groups of test scores, the pre-test and the post-test.   What if we wanted to find out if there was a difference between the pre- and post- test scores broken down by sex?

 Points Questions 4 points 24. How many groups are there for this analysis considering pre-test data, post-test data and sex?  Name them. 2 points 25.  What statistical test would propose to find out if there is a difference between these groups? 2 points 26.  What would your null hypothesis be for this additional analysis? 2 points 27.  What would your research hypothesis be for this additional analysis? 2 points 28.  In general, what conclusion could you draw from that statistical test? 2 points 29.  In general, what conclusion can’t you draw from this statistical test? 2 points 30.  What additional statistical test do you need to perform in order to find out where the actual difference lies?

Third statistical test (15 points):

In your first and second statistical tests you were trying to find out whether there was a difference between the way various groups performed on the SAME variable.  In this third scenario we want to find out whether there is a relationship between TWO different variables.

 Points Questions 2 points 31.  What statistical test do you propose to find out the relationship between post-test scores and the number of hours studied? 3 points 32.  What formula would you use to find the relationship between the post-test scores and the number of hours studied? 4 points 33.  Using this formula, what would your result be? 2 points 34.  How would you interpret your result? 2 points 35.  In general, what can you conclude from this statistical test? 2 points 36.  In general, what can’t you conclude from this statistical test?

Fourth statistical test (4 points):

Now, based on the result of the third test, we can conduct a further statistical test in order to see if we can make a suggestion to students about the number of hours they need to study in order to learn the most in their statistics course.

 Points Question 2 points 37.  What statistical test can we use to predict the number of hours a student needs to study in order to do well in statistics? 2 points 38.  Describe in words the interpretation you would be able to make based on this additional statistical test?