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STAT225 Spring 2014

Final Project

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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. 

If you have any questions about this assignment, please post them to the Questions about the Final Project main topic within the Final Project conference.

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.

Answer the following questions about this problem.

 

 

 

 

 

 

 

 

 

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):

Points

Question

2 points

12.  What statistical test are you going to use to find out whether there is a significant difference between the pre-test sample and the post-test sample?   Be specific. 

3 points

13.  Explain why this test is appropriate.  Include in your answer  three of the assumptions of the test you’re proposing and explain why each is important.

2 points

14.  What is the null hypothesis?

2 points

15.  What is the research hypothesis?

5 points

16.  Perform the calculations for your proposed statistical test and show your work and your answer.

2 points

17.  What is your observed value?

2 points

18.  What are your degrees of freedom?

2 points

19.  Is this a one-tailed or two-tailed test?

2 points

20.  What table are you going to use to find your critical value?  Please be specific and give the page number from Aron, Coups and Aron.

2 points

21.  What is your critical value?  Your p value should be .05.

2 points

22.  Based on your observed and critical values, is the difference between these two groups significant?

3 points

23.  What conclusion can you draw from your result?  State your conclusion in words, based on your null hypothesis.

 

 

 

 

 

 

 

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?