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Research on Balance and Fitness - Statistical Analysis and Hypothesis Testing

Selection of Random Sample

STEP 1: You are doing research on balance and fitness.  To complete this research you will need to determine a question that has a numerical response.  Identify a random sample of n = 15 men and n = 15 women.


NOTE: Though it is suggested, you do not have to separate your data by gender. You may choose another delineation such as (parents/non-parents; adults over age 30/ adults under age 30; athletes/ non-athletes; etc….). Be sure to identify this in your initial abstract.

You must answer this question: How do you establish that this sample is truly random?


STEP 2: Have each subject answer the question and give a numerical response.


(i) Create a List of data results. You may use Excel for this.
(ii) Create at least two Labeled charts or graphs. You should use Excel for this.


STEP 3: You will analyze your data and compute the following statistics for each group:


(i)   The Mean and standard deviation of the numbers
(ii)  The Median for the data
(iii)  The Mode for the data
(iv)  The 90% confidence interval of the mean


STEP 4: Construct a complete hypothesis test and determine if the two groups have significantly different responses using ? = 0.05.


STEP 5: Write a one page introduction to your research, discuss how you selected your sample (is it a random sample?) and write a one page conclusion.  Present your data in an organized manner. Submit a full written 


Written Report: 

This MUST include:

(i)  Title Page
(ii)  Abstract:  First paragraph that briefly summarizes the paper, the motivation for choosing your topic, and include a general comment about the conclusion. (Usually this is written last.)
(iii)  List of data results
(iv)  Statistical Measurements (From Step 3)

(v)  Description of what is happening in your data by making statistical measurements. Do not talk about what the data implies here. Just describe what is happening.  You will talk about what it implies in the conclusion section. The description of the data MAY include:

    (a) General Trends or patterns
    (b) Differences in measurements depending on stratification of data or over time.
    (c) Variation
    (d) Margin of Error and Confidence Interval
    (e) Experimental Probability and Probability Distribution Tables
    (f) Linear or Exponential model 


(vi) Complete hypothesis test to determine if the two groups have significantly different responses using ? = 0.05.
(vii) Labeled charts or graphs. Insert them where you discuss your findings and refer to the charts or graphs.
(viii) Conclusion. This MAY include:

    (a) Did the study achieve its goals?
   (b) Do the conclusions make sense? Can you rule out alternative explanations for the results? If the conclusions do make sense, do they have any practical significance?
    (c) Discussion on how the description of your data addresses your question. 
    (d) What the description of the data implies about the whole population.
    (e) Discussion of what confounding variables you would address if you did it again and what confounding variables are very difficult to address
    (f) Extrapolation by predicting what will happen in the future using your regression equation.
(ix) Include the survey (if you did one) with a link in the Appendix.
(x) Include the data as a table in the Appendix


Topic Suggestions for the project:



(a) How many pairs of jeans do you own?
(b) How many times did you eat out fast food last week?
(c) How many text messages did you send yesterday?
(d) How many bottles of water did you drink last week?
(e) How many times did you go to the theatre last month?
(f) How many times did you go to the gym last month?
(g) How much did you spend the last time that you went shopping?


Research Project Rubric:

Organization: Maximum of 10 points

Overall report is well organized, with a cover page, introductory page, discussion of sampling, all data is shown, statistics are clearly presented, and conclusion page (points are deducted for presentation, missing information)

Statistics: Maximum of 40 points

Mean for each group is correct (8 points) 

Standard deviation for each group is correct (8 points) 

Median for each group is correct (8 points) 

Mode for each group is correct (8 points)

Confidence interval of the mean for each is correct (8 points) 

Hypothesis Test: Maximum of 30 points

Null and Alternate Hypothesis are stated correctly (8 points)

Critical t value is correct (6 points)

Computation of the t statistic is correct (8 points) 

Decision regarding the hypothesis is correct (8 points) 

Conclusion regarding the hypothesis is correct (8 points) 

Writing: Maximum of 20 Points

Overall writing is thorough with correct grammar, punctuation,

spelling, and capitalization.

(points are deducted for quality and mechanics)

Extra Credit: Maximum of 5 points

Graphics, graphs, Wow me! 

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