Turn in the following typed (12 point) and stapled packet for your final project:
____
Cover sheet containing your name(s), class time, and the name of your study
____
Summary , which includes all items listed on summary checklist
____
Solution sheet neatly and completely filled out. The solution sheet does not need to be typed.
____
Graphic representation of your data , created following the guidelines previously discussed; include only graphs which are appropriate and useful.
____
Raw data collected AND a table summarizing the sample data (
n ,
$\overline{x}$ and
s ; or
x ,
n , and
p ’, as appropriate for your hypotheses); the raw data does not need to be typed, but the summary does. Hand in the data as you collected it. (Either attach your tally sheet or an envelope containing your questionnaires.)
Bivariate data, linear regression, and univariate data
Student learning objectives
The students will collect a bivariate data sample through the use of appropriate sampling techniques.
The student will attempt to fit the data to a linear model.
The student will determine the appropriateness of linear fit of the model.
The student will analyze and graph univariate data.
Instructions
As you complete each task below, check it off. Answer all questions in your introduction or summary.
Check your course calendar for intermediate and final due dates.
Graphs may be constructed by hand or by computer, unless your instructor informs you otherwise. All graphs must be neat and accurate.
All other responses must be done on the computer.
Neatness and quality of explanations are used to determine your final grade.
Part i: bivariate data
Introduction
____State the bivariate data your group is going to study.
Here are two examples, but you may
NOT use them: height vs. weight and age vs. running distance.
____Describe your sampling technique in detail. Use cluster, stratified, systematic, or simple random sampling (using a random number generator) sampling. Convenience sampling is
NOT acceptable.
____Conduct your survey. Your number of pairs must be at least 30.
____Print out a copy of your data.
Analysis
____On a separate sheet of paper construct a scatter plot of the data. Label and scale both axes.
____State the least squares line and the correlation coefficient.
____On your scatter plot, in a different color, construct the least squares line.
____Is the correlation coefficient significant? Explain and show how you determined this.
____Interpret the slope of the linear regression line in the context of the data in your project. Relate the explanation to your data, and quantify what the slope tells you.
____Does the regression line seem to fit the data? Why or why not? If the data does not seem to be linear, explain if any other model seems to fit the data better.
____Are there any outliers? If so, what are they? Show your work in how you used the potential outlier formula in the Linear Regression and Correlation chapter (since you have bivariate data) to determine whether or not any pairs might be outliers.
Part ii: univariate data
In this section, you will use the data for
ONE variable only. Pick the variable that is more interesting to analyze. For example: if your independent variable is sequential data such as year with 30 years and one piece of data per year, your
x -values might be 1971, 1972, 1973, 1974, …, 2000. This would not be interesting to analyze. In that case, choose to use the dependent variable to analyze for this part of the project.
_____Summarize your data in a chart with columns showing data value, frequency, relative frequency, and cumulative relative frequency.
_____Answer the following question, rounded to two decimal places:
Sample mean = ______
Sample standard deviation = ______
First quartile = ______
Third quartile = ______
Median = ______
70th percentile = ______
Value that is 2 standard deviations above the mean = ______
Value that is 1.5 standard deviations below the mean = ______
_____Construct a histogram displaying your data. Group your data into six to ten intervals of equal width. Pick regularly spaced intervals that make sense in relation to your data. For example, do NOT group data by age as 20-26,27-33,34-40,41-47,48-54,55-61 . . . Instead, maybe use age groups 19.5-24.5, 24.5-29.5, . . . or 19.5-29.5, 29.5-39.5, 39.5-49.5, . . .
_____In complete sentences, describe the shape of your histogram.
_____Are there any potential outliers? Which values are they? Show your work and calculations as to how you used the potential outlier formula in
Descriptive Statistics (since you are now using univariate data) to determine which values might be outliers.
_____Construct a box plot of your data.
_____Does the middle 50% of your data appear to be concentrated together or spread out? Explain how you determined this.
_____Looking at both the histogram AND the box plot, discuss the distribution of your data. For example: how does the spread of the middle 50% of your data compare to the spread of the rest of the data represented in the box plot; how does this correspond to your description of the shape of the histogram; how does the graphical display show any outliers you may have found; does the histogram show any gaps in the data that are not visible in the box plot; are there any interesting features of your data that you should point out.
Due dates
Part I, Intro: __________ (keep a copy for your records)
Part I, Analysis: __________ (keep a copy for your records)
Entire Project, typed and stapled: __________
____ Cover sheet: names, class time, and name of your study
____ Part I: label the sections “Intro” and “Analysis.”
____ Part II:
____ Summary page containing several paragraphs written in complete sentences describing the experiment, including what you studied and how you collected your data. The summary page should also include answers to ALL the questions asked above.
____ All graphs requested in the project
____ All calculations requested to support questions in data
____ Description: what you learned by doing this project, what challenges you had, how you overcame the challenges
Note
Include answers to ALL questions asked, even if not explicitly repeated in the items above.
Questions & Answers
If a random variable X takes only two values -2 and 1 such that 2 P[X=-
2]=P[X=1]=P, then find variance of x.
The lower class boundary is found by subtracting 0.5 units from the lowerclass limit and the upper class boundary is found by adding 0.5 units to the upper class limit. The difference between the upper and lowerboundaries of any class.
Ekene
The lower class boundary is found by subtracting 0.5 units from the lowerclass limit and the upper class boundary is found by adding 0.5 units to the upper class limit. The difference between the upper and lowerboundaries of any class.