Project #2579 - Statistics

 

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

 

 

 

Answer the following questions about this problem.

 

Preliminary information about the data

 

Question

1.  What is the head of the statistics department trying to find out?

2.  What are the variables of interest?

3.  What is the measurement scale of the each of the variables of interest?

4.  What is the mean of the pre-test scores?

5.  What is the median of the post-test scores?

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.)

7.  What is the range of the hours studied values?

8.  Can you calculate a mean for the sex of the students involved in this pilot study?  Explain your answer.

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.

10. Looking at just the pre-test scores, using the empirical rule, is the distribution of these scores normal?

11. State the percentages of the empirical rule, before you continue with the next 3 questions.

12.  How many of the values fall within 1 SD of the mean?

13.  How many of these values fall within 1 and 2 SD of the mean?

14.  How many of these values fall with 2 and 3 SD of the mean?

 

First statistical test

 

 

Question

15.  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? 

 

16.  Explain why this test is appropriate.  Include in your answer the three of the assumptions of the test you're proposing.

 

17.  What is the null hypothesis?

 

18.  What is the research hypothesis?

 

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

 

20.  What is your observed value?

 

21.  What are your degrees of freedom?

 

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

 

23.  What table are you going to use to find your critical value?

 

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

 

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

 

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

 

     

 

 

 

Second statistical test

 

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

 

 

Questions

27. How many groups are there for this analysis considering pre-test data, post-test data and sex?

 

28.  What statistical test would propose to find out if there is a difference between these groups?

 

29.  What would your null hypothesis be for this additional analysis?

 

30.  What would your research hypothesis be for this additional analysis?

 

31.  What conclusion could you draw from that statistical test?

 

32.  What conclusion can't you draw from this statistical test?

 

33.  What additional statistical test do you need to perform in order to find out where the actual difference lies?

 

     

 

 

 

Third statistical test

 

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

 

 

Questions

34.  What statistical test do you propose to find out the relationship between post-test scores and the number of hours studied?

 

35.  What formula would you use to find the relationship between the post-test scores and the number of hours studied?

 

36.  Using this formula, what would your result be?

 

37.  How would you interpret your result?

 

38.  What can you conclude from this statistical test?

 

39.  What can't you conclude from this statistical test?

 

     

 

 

 

Fourth statistical test

 

            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.

 

Question

40.  What statistical test can we use to predict the number of hours a student needs to study in order to do well in statistics?

41.  Describe in words the interpretation you would be able to make based on this additional statistical test?

 

 

 

Follow-up

 

Question

42.  Are there any other questions or any other data that you would want to ask that might help the department design better statistics courses?

 

 

 

Subject Mathematics
Due By (Pacific Time) 03/07/2013 08:00 pm
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