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Experiencing Statistics Assignments (ESA's)

(Updated October 10, 2014)

Contents
ESA 8
ESA 10

Rules for Submitting ESA's

Due dates for ESA's are shown on the class calendar for your section. (If an ESA is shown on a day, that is the day it is due.) You may always turn in ESA's before the due date.
ESA's are due on the dates shown whether or not Dr. Gurney asks for them in class.
With the exception of ESA 1, if you do not turn in an ESA by the due date, it will lose a point for each class period that starts after the due date.
If you are unable to turn in an ESA in class on the due date, you may turn it in at Dr. Gurney's office before the next meeting of this class without losing points for being late.
Write each ESA as if the reader will be one of your classmates who has not done that ESA and has no access to the assignment material.
When you submit an ESA for grading, you will either receive a numeric score for the ESA or you will be asked to "REDO" the ESA.
If an ESA submission is missing requested information, has a major error or enough minor errors - but it is still worth possible points - you will be asked to "REDO" it.
A "REDO" will be marked by the word "REDO" and a date - instead of a numeric score - at the start of the ESA.
To "REDO" an ESA, you just need to correct any errors or add any missing information. You DO NOT need to rewrite or reprint the entire ESA.
If you are asked to "REDO" an ESA, you have two class periods from the date written next to "REDO" to make the needed changes to the ESA. If you turn in a "REDO" more than two classes after the date shown by the "REDO", you lose a point for each class period that has started after the first two classes.
ESA’s that you are asked to "REDO" are worth no points until a corrected version has been resubmitted and assigned a numeric score.
If you receive a numeric score for an ESA, you cannot rework that ESA for more points.
If you are asked to "REDO" an ESA, it may still receive the full 5 points.
You must receive points for ESA 1 before you can receive points for many of the other ESA's.
Whether you must "REDO" an ESA or are trying to finish ESA's 10 through 12, the last possible day to turn in ESA's for points is the last Thursday before finals week.
You may work ESA's by hand or with computer software, but your work must be submitted on paper.
Turning in ESA’s on time and receiving some points is better than turning them in late and receiving no points.

ESA Descriptions: Each of the twelve ESA’s is described below.

ESA 1: Hand Measurements and Favorite Colors

For each of 32 adult residents of the United States, do the following. One of the adult residents should be yourself.

a) Assign the subject an identifying number.
b) Measure and record their left hand span.
c) Measure and record their right hand span.
d) Measure and record their right thumb length.
e) Record their favorite color.

Make your measurements to the nearest tenth of a centimeter. Put the information you gather in a table with column headings "Subject Number", "Left Hand Span", "Right Hand Span", "Right Thumb Length", and "Favorite Color".

Mark the row containing the measurements you made on yourself with a star or asterisk.

NOTE: If you measure correctly, most of the digits from 0 to 9 should appear to the right of the decimal point for each of your handspan measurements, and also for your thumb length measurements. Also, the left hand span is usually NOT the same as the right hand span for a subject.

You must receive credit for ESA 1 before you can receive credit for many of the other ESA’s. Once you receive credit for ESA 1, you should make a copy of it and keep the copy in a safe place, because you will need the information from ESA 1 for many of the following ESA's.

Table Forms for ESA 1 Excel File Word File PDF File

ESA 2: Semester Project Data

For this ESA, you will choose your semester project data set. Your data set should contain three columns of measurement data, and one column of categorical data, and there should be at least 32 items in each column.

Two of the measurement variables should measure similar things or have a similar range of values. These will be your comparable variables. Examples would be a student's grade point average for two different semesters, or the number of points a basketball player scores in two different seasons. The third measurement variable can be almost anything, but it should be different than the first two.

The categorical variable should have at least four possible values. When using weather data, the outlook is categorical and four possible values are sunny, rainy, cloudy, and thunderstorms. When looking at movies, the producers are categorical and four possible values are Paramount, 20th Century Fox, Dreamworks, and Screen Gems.

Some examples of categorical and measurement varibles are available in the Categorical vs Measurement section of this website. Examples of acceptable project data sets are also found in the Semester Project Information section of this website. You MAY NOT use the data sets in the textbook, or the sample project data sets or data from the sample semester project on the website, and you may not use ESA 1 data for ESA 2, but you may use similar data sets.

You may obtain your data from newspapers, magazines, scholarly journals or the internet. Books are not allowed. You will need to state the source of your data. For newspapers, magazines and journals, include the title, the issue of the publication (volume and issue number or date published), and the page numbers. For websites, include the name of the website, the web address, and the date you obtained the data from the website (This is the date the data was accessed). Be specific when referencing websites, if your data is not on the homepage of the website, then you will need to reference the subpage of the website where you found your data.

You should usually have between one and four sources for your data. Usually, you can find all the values for one variable in a single location. Sometimes all the data needed can be found in one location, but most students need to use two or more sources to obtain all the necessary data.

You may use search engines like Google to find data on the internet, but your data source or sources will have to be one or more websites that result from your searches.

You will need to create a single table containing all of your data. If you cannot fit all of your data on one or two pages, you are doing something very wrong. A complete ESA 2 will contain this table along with the sources of information for your data.

Table Forms for ESA 2 Excel File Word File PDF File

The following are general descriptions of some data sets you could use.

a) The weather for 32 different cities around the country or around the world. Use the high temperature for two different days for two of your measurement variables, and then use something else like the low temperature or humidity on one day for the third mesurement variable. Use the outlook for one of the days (rainy, sunny, cloudly, thunderstorms) as your categorical variable. Instead of high temperature, you could use low temperature or precipication.
b) The top 32 players in a sport. For the categorical variable,you could use the team they play for or their position. For the two similar measurement variables, you can use the points they score in two different games or two different seasons. Instead of points scored, you could use something like assists per game or their scoring percentages in two different seasons. Something else like salary or weight could be used as the third measurement variable.
c) The top 32 money-making movies for two consecutive weeks. Use the production company as the categorical variable. Use the money earned during each of the two weeks as your comparable measurement variables. Use the number of theaters or the number of tickets sold for one week as the other measurement variable. Something similar could be done for music or video games.
d) Look at stock prices for 32 different companies. The categorical variable could be the type of company such as retail, manufacturing, software, mining, etc. The two similar measurement variables could be the stock prices on two consecutive days. You could also look at changes in stock prices over two consecutive days or over two consecutive months. The third measurement variable could be the average stock price for the last quarter or last year, or the number of shares sold.
e) Collect your own data. Just make sure you have one categorical variable with at least four possible values and three measurement variables, and that two of the measurement variables are measuring similar things. IF YOU DO GATHER YOUR OWN DATA, MAKE SURE THAT YOUR DATA COLLECTION METHOD DOES NOT VIOLATE THE RIGHTS OR HURT THE WELFARE OF PEOPLE OR ANIMALS.

A blank row or column element WILL NOT count as one of the 32 items you need for your variables.

Use sources of data that are less than six months old.

I do like to encourage creativity, so if you come up with a data source unlike anything I have seen before, I will give you up to 4 bonus points for originality.

If you have a data set you would like to use that does not fit all the requirements given above, check with me. I will either tell you how to adapt the data to the project, or give you permission to use your data set as is.

If you have not received credit for ESA 2 by the last day to drop for this semester, you will receive no points for ESA 2 and I will choose your semester project data for you.

If you want to change your project data after you receive points for ESA 2 or have been assigned a data set by me, you will need my approval.

If you change your data without my approval and your data set does not meet the criteria given above, you will lose 10 points from your semester project score.

You will receive no additional points for ESA 2 if you change your data set after ESA 2 has received a numeric score.

ESA 3: Categorical Frequency Distribution and Bar Chart

Do the following with the favorite color data obtained in ESA 1.

a) Create a categorical frequency distribution showing the frequency and relative frequency of each color.
b) Create a bar chart showing the frequency of each color. The bar chart should be at least 10 centimeters high by 15 centimeters wide.

ESA 4: Quantitative Frequency Distribution and Histogram

Using the right thumb length data from ESA 1, do the following.

a) Create a quantitative frequency table with five classes.
b) Create a histogram from your frequency table in part (a). This graph should be at least 10 centimeters high by 15 centimeters wide.
c) Write a paragraph in which you answer all of the following questions about the histogram you created for part (b) above.
What is the biggest data value?
What is the smallest data value?
Is the histogram skewed-left, skewed-right, bell-shaped, uniform, or symmetric; or does it have no special shape?
How many peaks does the histogram have, and where are they located?
Does the histogram have any gaps and, if so, where?
Does the histogram have any extreme values and, if so, where?

See the Quantitative Frequency Distribution and Histogram section of this website for information on the various aspects of this ESA.

ESA 5: Basic Statistics

Using the right thumb length data from ESA 1, find the following.

mean
first quartile
range
mode
median
standard deviation
midrange
third quartile
interquartile range

ESA 6: Modified Boxplots

Using the left hand span and right hand span data you obtained in ESA 1, do the following.

a) Find the minimum value of both your left and right handspan data. Find the maximum value of both your left and right handspan data. Make a uniform number scale extending from the minimum found above to the maximum found above. This scale should be at least 15 centimeters long. Leave room for two boxplots on the page above this number scale.
b) Make a modified boxplot of your left handspan data and a modified boxplot of your right handspan data. Put both boxplots above the number scale created in (a). One boxplot should be higher on the page than the other so that they do not overlap. WARNING: When you are finished you will have drawn two boxplots and just one number scale.
c) Write a paragraph in which you answer all of the following questions about the pair of boxplots you created for part (b) above.
Which boxplot has the biggest value?
Which boxplot has the smallest value?

Which boxplot has the largest range?

Which boxplot has the largest interquartile range?
Which boxplot has the largest median?
Which boxplot is more skewed?

See the Comparing Boxplots section of this website for information on the various aspects of this ESA.

ESA 7: Thumb Tack Experiment

First obtain a thumb tack. The two figures below illustrate a thumb tack from two different perspectives. Dr. Gurney usually carries thumb tacks in his book bag.

Thumb tack with point up Thumb tack with point down

Then find a sooth level surface like a desk top or a linoleum floor, and do the following.

a) Make a table with 100 rows and the following four columns "Toss Number", "Result", "Cumulative Ups" and "Percent Up"
b) Toss the thumb tack on the level surface.
c) Record the toss number in the Toss Number column.
d) Record the result - "Up" or "Down" - in the Result column.
e) Record the total number of ups as of that toss in the Cumulative Ups column.
f) Record the percent up as of that toss in the Percent Up column. Percent Up is found by dividing the Cumulative Ups by the Toss Number and then multiplying the result by 100%.
g) Go back and repeat parts (b) through (f) until you have tossed the thumb tack 100 times and filled in all four columns of the table for each toss.
h) Make a time series plot of the Percent Up versus the Toss Number. Toss Number will take the role of time unit for your graph, and Percent Up will be on the vertical scale. The graph should be at least 15 centimeters high by 25 centimeters wide. Use the longer dimension of the paper for the Toss Number axis and the shorter dimension for the Percent Up axis. You may tape sheets of paper together and/or use graph paper for this assignment.
i) State the empirical probability that the point will land up.

See the Die Toss section of this website for an experiment with data recorded in a similar table and a similar plot of percent versus toss number.

WARNING: DO NOT use a push pin for this ESA. A push pin is not a thumb tack. The figures below illustrate a push pin from two different perspectives.

Push pin with point up. Push pin on its side.

ESA 8: Curving Grades

In this ESA, you will be "curving" the Test 2 scores from your class. You will find the Test 2 score distribution on Moodle in the same location as the syllabus and the chapter notes. See the Curving Grades section of this website for examples of how to curve test scores.

a) Find the mean and standard deviation for the Test 2 scores.
b) Find the cutoff scores for an A, a B, a C and a D, assuming the test scores are normally distributed and the top 10% receive A’s, the next 10% receive B’s, the next 10% receive C’s and the next 10% receive D’s.
c) State your own Test 2 score and determine what letter grade you would receive with the cutoffs found in part (b).
d) Say whether or not you like the way your grade would be “curved” with these cutoffs.

ESA 9: Confidence Interval for Mean

Use your right thumb length statistics from ESA 5 to find and state the 95% confidence interval for the population mean of right thumb lengths for adult residents of the United States. State the values of any quantities you needed to do this computation. Finally, give an interpretation of your confidence interval.

ESA 10: Sample Size for Proportion

Use your favorite color data from ESA 1 to find the minimum sample size needed to estimate the proportion of adult residents of the United States whose favorite color is blue to within 3 percentage points with 95% confidence. State the formula you use and the values of any quantities you needed to do this computation.

ESA 11: Hypothesis Test of the Mean

Use your right thumb length statistics from ESA 5 to test the claim that the population mean for right thumb lengths of adult residents of the United States is more than 5.5 cm at 95% confidence. State the test statistic, the P-value, the values of any quantities you needed to do this test, and your conclusion in English.

ESA 12: Matched Pairs Test

Using the left hand span and right hand span data you obtained in ESA 1, run a matched pairs test to see if the mean of left hand spans equals the mean of right hand spans at 95% confidence. State the test statistic, the P-value, the values of any quantities you needed to do this test, and your conclusion in English.

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