Download Single-sample t-test with Caramel Apple Pops PDF

Title of Resource Stats Lab: Single-sample t-test with Caramel Apple PopsTM
Author(s) Maya G. Sen
Institution Northern Michigan University
This hands-on activity has students collect data that they analyze (by hand
and with SPSS) using a single-sample t-test. They compare the weights of a
Brief Description:
sample of Caramel Apple PopsTM to the population mean (i.e., the
advertised weight).
Keywords: Single-sample t-test, SPSS calculation, interpretation of findings
Author Contact
[email protected], www.mayasen.com
Information:
Additional
Information:
TeachPsychScience.org is made possible with grant support from the Association for Psychological
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(www.teachpsychscience.org/submissions).
© 2013 by Maya G. Sen . All Rights Reserved. This material may be used for noncommercial
educational purposes. All other uses require the written consent of the authors.
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Notes





I have found some packages with advertised weights of 17.0g, and others post the
weight as 17.7g.
I have done this lab several times in class, and each time the average weight was
significantly higher than advertised.
If I feel that the class has mastered calculating sums of squares, I will calculate that for
them. If it’s a group that is still struggling, I will have them calculate it for more practice.
Once I have sent them the data, I wander around the classroom to give help as needed.
We then go over the results as a class, so they can check their calculations against mine.
This activity takes approximately one 50-minute class period (although I sometimes
have to go a little over – my classes are 100 minutes).
Materials Needed


Enough Caramel Apple PopsTM for everyone (including you!).
o You can substitute other candy that has its weight listed on the individual pieces,
but Caramel Apple PopsTM are very popular with the students.
o http://www.amazon.com/Caramel-Apple-Pops-48-CountPackage/dp/B0015AWU7U/
A small scale, e.g., http://www.amazon.com/gp/product/B0012N1NAA/
Single-sample t-test Lab
Notes





I have found some packages with advertised weights of 17.0g, and others post the
weight as 17.7g.
I have done this lab several times in class, and each time the average weight was
significantly higher than advertised.
If I feel that the class has mastered calculating sums of squares, I will calculate that for
them. If it’s a group that is still struggling, I will have them calculate it for more practice.
Once I have sent them the data, I wander around the classroom to give help as needed.
We then go over the results as a class, so they can check their calculations against mine.
This activity takes approximately one 50-minute class period (although I sometimes
have to go a little over – my classes are 100 minutes).
Materials Needed


Enough Caramel Apple PopsTM for everyone (including you!).
o You can substitute other candy that has its weight listed on the individual pieces,
but Caramel Apple PopsTM are very popular with the students.
o http://www.amazon.com/Caramel-Apple-Pops-48-CountPackage/dp/B0015AWU7U/
A small scale, e.g., http://www.amazon.com/gp/product/B0012N1NAA/
Single-sample t-test Lab
Goals: The goals of this lab are 1) to give you experience collecting and analyzing data using the
single-sample t-test, and 2) to help you understand the purpose and appropriate use of the
single-sample t-test.
Background: The single-sample test is used when a researcher has data from one sample, and is
comparing that sample to a population mean (remember, the population standard deviation is
unknown for t-tests, and therefore must be estimated based on the sample’s SD). In this lab, we
will compare the weights of a sample of Caramel Apple PopsTM to their advertised weight
(17.0g), which we will treat as the population mean. (We’ll assume that the company weighed a
population’s-worth of their candy, and that the advertised weight is that population mean.)
Instructions: Go to the front of the classroom, grab a Caramel Apple Pop TM, and weigh it. Tell
me its weight so that I can enter it into the spreadsheet.
Note: I will subtract 1g from each weight to account for the weight of the wrapper and
the stick (previous years’ students have weighed numerous sticks + wrappers, and they
have averaged 1g). To save time, we will not weigh the stick and wrapper from each
individual.
While the rest of the class weighs their candy and I prepare the spreadsheet, get started on the
steps of the hypothesis-testing procedure (the parts you can do without our data). Work in
pairs or groups of three.
When the data are collected, I will send you a spreadsheet. Complete the hand calculations to
test your hypothesis. Once you are done, redo the calculations in SPSS to double-check your
work.
Step 1: Identify the correct comparison distribution and statistical analysis to use:
Analysis: Single-sample t-test
Comparison Distribution:
Step 2: State the research hypothesis and null hypothesis for a two-tailed test.
State your H1:
State your H0:
Step 3: Determine the characteristics of the comparison distribution.
a. Mean of comparison distribution (NOT the mean of your sample) =
b. Calculate the standard deviation of the comparison distribution as follows:
Estimated population standard deviation
s=
Standard deviation of the distribution of means
c. The shape is a t distribution with
sM =
degrees of freedom (df).
Step 4: Determine the critical value(s) on the comparison distribution.
a. Set the significance level at 0.05. This is a two-tailed test.
b. The appropriate cut-off scores (tcrit) are:
Step 5: Calculate your t-test.
tobt =
Step 6: Decide whether to reject H0.
REJECT or FAIL TO REJECT H0? (circle the correct one)
Step 7: Calculate effect size, and circle the strength of the effect size.
d=
The effect size is [none, small, medium, large].
Step 8: Write a summary statement. Fill in the blanks and circle where appropriate.
A single sample t-test was performed to determine whether the mean weight of the
Caramel Apple PopsTM differed from the advertised weight of 17.0g. The mean weight [did/
did not] differ significantly from the advertised weight, t(
with a
effect size (d =
)=
).
How do you think the company would respond to these results? Why?
,p
0.05,
Step 9: Now, run the analysis in SPSS to double-check your answers. Be sure to look carefully at
your output to ensure you understand where to find the relevant information.

Copy and paste your data from Excel into SPSS (the “Data View” tab).

On the “Variable View” tab, label your variable, set the decimal places to “1,” and select
“Scale.”

Select Analyze > Compare Means > One-Sample T Test…

Move your variable from the box on the left to the right using the center arrow key.

Set the Test Value to 17.0 (the population mean).

Click OK.

Your output should look like the example below (although the numbers will be
different).

You should be able to find several numbers that match the numbers you calculated.
Remember, since SPSS can more easily keep track of many decimal places than we can,
that the number may not be identical. They should, however, be close. Look for the
following:
o N, Mean, s, sM, t, df, and p
o Do your results match SPSS’s results?
Single-sample t-test Lab KEY
Goals: The goals of this lab are 1) to give you experience collecting and analyzing data using the
single-sample t-test, and 2) to help you understand the purpose and appropriate use of the
single-sample t-test.
Background: The single-sample test is used when a researcher has data from one sample, and is
comparing that sample to a population mean (remember, the population standard deviation is
unknown for t-tests, and therefore must be estimated based on the sample’s SD). In this lab, we
will compare the weights of a sample of Caramel Apple PopsTM to their advertised weight
(17.0g), which we will treat as the population mean. (We’ll assume that the company weighed a
population’s-worth of their candy, and that the advertised weight is that population mean.)
Instructions: Go to the front of the classroom, grab a Caramel Apple PopTM, and weigh it. Tell
me its weight so that I can enter it into the spreadsheet.
Note: I will subtract 1g from each weight to account for the weight of the wrapper and
the stick (previous years’ students have weighed numerous sticks + wrappers, and they
have averaged 1g). To save time, we will not weigh the stick and wrapper from each
individual.
While the rest of the class weighs their candy and I prepare the spreadsheet, get started on the
steps of the hypothesis-testing procedure (the parts you can do without our data). Work in
pairs or groups of three.
When the data are collected, I will send you a spreadsheet. Complete the hand calculations to
test your hypothesis. Once you are done, redo the calculations in SPSS to double-check your
work.
Step 1: Identify the correct comparison distribution and statistical analysis to use:
Analysis: Single-sample t-test
Comparison Distribution: sampling distribution of the mean
Step 2: State the research hypothesis and null hypothesis for a two-tailed test.
State your H1: Our sample of CA Pops will weigh more or less than the advertised weight
(17.0g).
M≠μ
State your H0: The weight of our CA pops will not differ from the advertised weight (17.0g).
M=μ
Step 3: Determine the characteristics of the comparison distribution.
a. Mean of comparison distribution (NOT the mean of your sample) = 17.0
b. Calculate the standard deviation of the comparison distribution as follows:
Estimated population standard deviation
s=
Standard deviation of the distribution of means
c. The shape is a t distribution with
20
0.468
sM =
0.102
degrees of freedom (df).
Step 4: Determine the critical value(s) on the comparison distribution.
a. Set the significance level at 0.05. This is a two-tailed test.
b. The appropriate cut-off scores (tcrit) are:
±2.086
Step 5: Calculate your t-test.
tobt = (18.181-17)/0.102 = 11.58
Step 6: Decide whether to reject H0.
REJECT or FAIL TO REJECT H0? (circle the correct one)
Step 7: Calculate effect size, and circle the strength of the effect size.
d = (18.181-17)/0.468 = 2.53
The effect size is [none, small, medium, large].
Step 8: Write a summary statement. Fill in the blanks and circle where appropriate.
A single sample t-test was performed to determine whether the mean weight of the
Caramel Apple PopsTM differed from the advertised weight of 17.0g. The mean weight [did/
did not] differ significantly from the advertised weight, t( 20 ) = 11.58, p < 0.05, with a large
effect size (d = 2.53).
How do you think the company would respond to these results? Why?
They may be pleased because the sample we studied weighed more than the advertised
weight, indicating that they are not cheating their customers. However, the company may
prefer that we had found no significant difference from the advertised weight, so that they
are not using more ingredients than necessary, which would cost them extra money.
Step 9: Now, run the analysis in SPSS to double-check your answers. Be sure to look carefully at
your output to ensure you understand where to find the relevant information.

Copy and paste your data from Excel into SPSS (the “Data View” tab).

On the “Variable View” tab, label your variable, set the decimal places to “1,” and select
“Scale.”

Select Analyze > Compare Means > One-Sample T Test…

Move your variable from the box on the left to the right using the center arrow key.

Set the Test Value to 17.0 (the population mean).

Click OK.

Your output should look like the example below (although the numbers will be
different).

You should be able to find several numbers that match the numbers you calculated.
Remember, since SPSS can more easily keep track of many decimal places than we can,
that the number may not be identical. They should, however, be close. Look for the
following:
o N, Mean, s, sM, t, df, and p
o Do your results match SPSS’s results? (The one below is the example. The next
page has the answers for our data.)