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Experiencing Statistics Assignments (ESA's)

(Last updated December 21, 2019)

Contents
ESA 8
ESA 10
ESA 13 ESA 14

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 calendar date, that is the date it is due.)
ESA's are due on the dates shown whether or not Dr. Gurney asks for them in class.
You may always turn in ESA's before the due date.
ESA's 1 and 2 are special in that they must be submitted as e-mail attachments and they are the only ESA's that will be submitted as e-mail attachments. Just like the other ESA's, these ESA's may receive REDO's, and you won't receive credit for these ESA's until they are completed in an acceptable fashion.
For ESA's 3 and later, you may work the ESA's either by hand or with computer software, but your work must be submitted on paper.
You must receive points for ESA 1 before you can receive points for many of the other ESA's.
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. Thus, again with the exception of ESA 1, ESA's that have not been turned in within three weeks of the due date are worth no points.
If you are unable to turn in an ESA in class on or before 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.
Whether you must "REDO" an ESA or are trying to finish ESA's 10 through 14, the last possible day to turn in ESA's for points is the last Thursday before finals week.
All graphs that are required for an ESA should be created using a statistical software program like Minitab, SPSS or R.
Write each ESA as if the reader is one of your classmates who has not started 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 those 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, that ESA may still receive the full 5 points.
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 fourteen 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.

i) Assign the subject an identifying number.
ii) Measure and record their left hand span.
iii) Measure and record their right hand span.
iv) Measure and record their right thumb length.
v) Record their favorite color.

Make your measurements to the nearest tenth of a centimeter. Put the information you gather in an Excel spreadsheet 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 by using bold, italicized font.

Send the completed EXCEL spreadsheet as an e-mail attachment to Dr. Gurney at dgurney@selu.edu with "ESA 1" as the subject. DO NOT encrypt or condense the file.

To receive points for ESA 1, you must have all the requested data in the correct format. If you have completed ESA 1 correctly, you will receive an e-mail with "5 PTS" in the subject heading. If not, you will receive an e-mail with "REDO" in the subject heading and a list of items that must be corrected.

NOTE 1: 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.

NOTE 2: You must receive credit for ESA 1 before you can receive credit for many of the other ESA’s.

Excel Form for for ESA 1

ESA 2: Semester Project Data

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

Two of the quantitative variables should have similar values. That is most of the values of both these variables should be about the same size, and some of the values of the first variable should be smaller than the corresponding values of the second variable, while some of the values of the first variable should be larger than the corresponding values of the second variable. These two variables 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 quantitative variable can be almost anything, but it must be different than the first two.

Use at most four significant digits for your quanitative data. If a variable has large values, you may need to record the values in thousands, or millions, or billions, etc.

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

Some examples of qualitative and quantitative varibles are available in the Qualitative vs Quantitative 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. You may, however, use data that is similar to any of these data sets.

You may use 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 the website or websites that result from your searches.

You will need to create a single table containing all of your data in an Excel spreadsheet. You should be able to fit all of your data on one or two printed pages. Otherwise, you are doing something very wrong. A complete ESA 2 will include the table containing all your data and the source or sources of information for your data.

Send the completed EXCEL spreadsheet as an e-mail attachment to Dr. Gurney at dgurney@selu.edu with "ESA 2" as the subject. DO NOT encrypt or condense the file.

To receive points for ESA 2, you must have all the requested data in the correct format along with the source information and the source date. If you have completed ESA 2 correctly, you will receive an e-mail with "5 PTS" as the subject. If not, you will receive an e-mail with "REDO" as the subject and a list of items that must be corrected.

Otherwise, you will receive a REDO and there will be a note in Moodle listing the items that must be corrected.

Excel Form for ESA 2

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 quantitative variables, and then use something else like the low temperature or humidity on one day for the third quantitative variable. Use the outlook for one of the days (rainy, sunny, cloudly, thunderstorms) as your qualitative variable. Instead of high temperature, you could use low temperature or precipication.
b) The top 32 players in a sport. For the qualitative variable,you could use the team they play for or their position. For the two similar quantitative 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 quantitative variable. DO NOT USE NFL QUARTERBACKS - Since there are only 32 teams, there are usually not much more than 32 quarterbacks playing in a given season. College quarterbacks, however, would be fine for this ESA.
c) The top 32 money-making movies for two consecutive weeks. Use the production company as the qualitative variable. Use the money earned during each of the two weeks as your comparable quantitative variables. Use the number of theaters or the number of tickets sold for one week as the other quantitative variable. Something similar could be done for music or video games.
d) Look at stock prices for 32 different companies. The qualitative variable could be the type of company such as retail, manufacturing, software, mining, etc. The two similar quantitative 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 quantitative 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 qualitative variable with at least four possible values and three quantitative variables, and that two of the quantitative 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 WELFARE OF PEOPLE OR ANIMALS.

A blank row element 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 requirements, 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. There will be no change to your ESA 2 score if you change your data set after ESA 2 has received a numeric score.

If you change your data without my approval and your data set does not meet the criteria given above, you will lose 20 points from your semester project score.

Note: ESA 2 is not intended to be difficult, but this is the ESA that most students have trouble completing. The good news is that you do not need a numeric score for ESA 2 to receive points for ESA 3 or later.

ESA 3: Qualitative Frequency Distribution and Bar Chart

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

1) Create a qualitative frequency distribution showing the frequency and relative frequency of each color.
2) Using a statistical software program like Minitab, SPSS or R, create a bar chart showing the frequency of each color. Your bar chart should have the following:
a) a descriptive title,
b) a subtitle saying that you created the bar chart
c) horizontal gridlines, and
d) a label for the vertical (frequency) scale.

ESA 4: Histogram

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

1) Using a statistical software program like Minitab, SPSS or R, create a histogram from your right thumb length data that has exactly FIVE classes. Your histogram should have
a) a descriptive title,
b) a subtitle saying that you created the histogram,
c) horizontal grid lines
d) a label for the vertical (frequency) scale, and
e) the horizontal axis should have a descriptive label which includes the units of measure.
2) Write a paragraph in which you answer all of the following questions about the histogram you created for part (1).
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

Create and fill in a table with the format shown below using your left handspan data, your right handspan data, and your right thumb length data.

 

Left Hand Span

Right Hand Span Right Thumb Length
Mean      
Mode      
Minimum      
First
Quartile
     
Median      
Third Quartile      
Maximum      
Range      
Interquartile Range      
Standard Deviation      

Standard Error of
the Mean

     
Skewness      

ESA 6: Paired Horizontal Boxplots

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

1) Using a statistical software program like Minitab, SPSS or R, make a pair of HORIZONTAL boxplots in the same frame. One boxplot will be of your left handspan data and the other boxplot will be of your right handspan data. When you are finished, you should have both boxplots over a single number line. Your paired boxplots should have ,
a) a descriptive title,
b) a subtitle saying that you created the boxplots,
c) vertical grid lines, and
d) a descriptive label for the horizontal axis including the units of measure.
2) Write a paragraph in which you answer all of the following questions about the pair of boxplots you created for part (1) 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: Scatter Diagram

1) Using a statistical software program like Minitab, SPSS or R, make a scatter diagram of your right hand span and right thumb length data showing the regression line. Your scatter diagram should have:

a) a descriptive title,
b) subtitle saying that you created the scatter diagram
c) both vertical and horizontal grid lines, and
d) descriptive labels for both axes, showing the units of measure for each axis.

2) State the equation of the regression line in the form y = a + bx where you have substituted numbers for both a and b.

3) State and interpret the value of R-square for your scatter diagram.

4) Write a paragraph which contains the following information about your scatter diagram.

State whether the data shows a positive or negative association, and also whether the association is strong, moderate or weak.
Identify any outliers on the scatter diagram.
Identify any influential observations on the scatter diagram.

ESA 8: 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

Next, find a smooth level surface like a table top or a linoleum floor, and do the following.

1) Make a table with 100 rows and the following four columns "Toss Number", "Result", "Total Ups" and "Percent Up"
2) Toss the thumb tack on the level surface.
3) Record the toss number in the Toss Number column.
4) Record the result - "Up" or "Down" - in the Result column.
5) Record the total number of ups as of that toss in the Cumulative Ups column.
6) Record the percent up as of that toss in the Percent Up column. Percent Up is found by dividing the Total Ups by the Toss Number and then multiplying the result by 100%.
7) 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 of the 100 tosses.
8) Using a statistical software program like Minitab, SPSS or R, 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. Your time series plot should also have (i) a descriptive title, (ii) a subtitle saying you are the creator of the time series plot, and (iii) vertical and horizontal grid lines.
9) Last but not least, state your estimate for the probability that the point of the thumb tack will land up.

You will need to turn in (i) your complete table of data, (ii) the time series plot of your results, and (iii) your estimate for the probability of the point landing 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.

NECESSARY FORMULA: Percent Up = (Total Ups)/(Toss Number) x 100%

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 9: 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.

1) Find the mean and standard deviation for the Test 2 scores.
2) 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. Show your calculations or the calculator function with the numbers used to reach each of these results.
3) State your own Test 2 score and determine what letter grade you would receive with the cutoffs found in part (2).
4) Finally, say whether or not you like your grade after it has been “curved” using these cutoffs.

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 4 percentage points at 95% confidence. As part of your answer state the following:

1) the formula that you used,
2) the values of any quantities that you needed to do this computation, and
3) the minimum sample size that you computed.

ESA 11: Confidence Interval for Mean

Use your right thumb length statistics from ESA 5 to find the 95% confidence interval for the population mean of right thumb lengths for adult residents of the United States. As part of your answer, do the following:

1) state the mean of your right thumb length measurements
2) state the standard deviation of your right thumb length measurements
3) state the 95% confidence interval for the population mean of right thumb lengths for adult residents of the United States, and
4) interpret what your confidence interval means.

ESA 12: 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 in the United States is more than 5.6 cm at 95% confidence. As part of your answer, state the following:

1) the mean of your thumb length measurements,
2) the standard deviation of your thumb length measurements,
3) the test statistic,
4) the P-value, and
5) your conclusion in English.

ESA 13: Dependent Difference Test

Use your left hand span and right hand span data from ESA 1 to test the claim that there is no difference between the means of the left hand span and right hand span at 95% confidence. As part of your answer, state the following:

1) the mean of the differences between the left and right hand spans,
2) the standard deviation of the differences between the left and right hand spans,
3) the test statistic,
4) the P-value, and
5) your conclusion in English.

ESA 14: Hypothesis Test for Significant Linear Correlation

Test to see if there is significant linear correlation between your right thumb lengths and your right handspans at 95% confidence. As part of your answer, state the following:

1) the correlation coefficient between your right thumb lengths and your right hand spans,
2) the test statistic,
3) the P-value, and
4) your conclusion in English.

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