Average Length of Last Names
Synopsis: An activity which involves testing a hypothesis about
a population mean when the population standard deviation is not known.
Students break up into groups (samples) of size 4, and perform the hypothesis
test based on their sample data. The random variable of interest is the
number of letters in a student's last name.
Type of activity: In-class, small-group
Statistical topics: sample mean, standard deviation, standard
error of the mean, t-test
Time needed: 20 minutes
Materials needed:
-
An activity form (Word97 Version, PDF
Version) for collecting data
-
An assistant to collect the forms and enter the results in a computer file
for analysis
Procedure:
Part I
-
Ask students to break up into groups of size 4 (in any event, no less than
3 nor more than 6 students per group).
-
Give one activity form to each group.
-
Ask students to determine the number of letters in each of their last names,
and record data on the activity form.
-
With the instructor specifying the null hypothesis and the significance
level, ask the students to complete the calculations on the form. (A good
value for the mean under the null hypothesis is the number of letters in
the instructor's name. That is, if the instructor has 8 letters in his
last name, set the null hypothesis mean at 8.)
-
Note that the instructor may want to make up data and go through the procedure
once with the students, so that the students are reminded of the formulas
and calculations.
Part II
-
When students are finished, have assistant collect the forms and enter
the test statistics into a software package for analysis.
-
Instructor can use the entered data to calculate the proportion of times
the null hypothesis is rejected.
-
Instructor can use a software package to calculate p-values for various
values of t obtained by the students.
Comments from others who have tried activity: None.
Supplementary materials: Activity Form: Word97
Version. PDF Version.
This activity was submitted by William L. Harkness: wlh@stat.psu.edu