Sampling Error
In order to be able to accurately project the results of a survey question from the sample
to the entire population of the target market, the correct sample size must be used. The
correct sample size can be calculated using this formula:
Z 2  2
n
E2
in which:
n = Sample Size
Z = Level of Significance (Expressed as a Z-Score)
 = Population Standard Deviation (2 = Population
Variance)
E = Acceptable Amount of Sampling Error
The Z-score in this equation can be looked up from a table that shows the probability of a
sample error. An example of this is the table of Z-values contained in the back of the
textbook. Generally, for this class and in practice we always use the probability of a
sample error to be 0.10 or 0.05. A probability of a sample error of 0.10 has an associated
Z-score of 1.645. A probability of a sample error of 0.05 has an associated Z-score of
1.96.
The acceptable amount of sampling error is something that must be determined by
management. The more accurate management wants the survey results to be, the smaller
the amount of sampling error has to be. You may suggest an amount of sampling error,
but the final decision on this value should generally be left up to management. One
reason for this is that the smaller the amount of sampling error is, the larger the sample
size will need to be. A bigger survey costs more to conduct, and management needs to
weigh this cost in determining the amount of sampling error.
Assignment and Example: So that we can better understand what a sample error is and
its possible effects on our projects, we are going to now look at the following assignment
and example.
Assignment Example:
1. We found eight students (either MBA or Undergrad Students) who have taken the
GMAT.
2. We wrote down the students’ names and scores.
3. We then created as many possible groups of three students with their scores from
these eight students. For example, if the names I collected were Bill (690), Tim
(590), Natalie (780), Sarah (630), Mark (760), Andrew (720), Steve (580), and
Alice (600) then four of my groups of three are going to look like this:
-Bill (690)
-Tim (590)
-Natalie (780)
-Bill (690)
-Tim (590)
-Sarah (630)
-Bill (690)
-Tim (590)
-Mark (760)
-Bill (690)
-Tim (590)
-Andrew (720)
Record all possible groups of three (Use the Sampling Error Excel Grid found in
the “Courses” folder). There should be a total of 56 groups.
4. Create a histogram to show the distribution of your samples. (Use ranges for your
columns in your histogram. For example, 580-600, 601-620, 621-640, 641-660,
661-680, 681-700, 701-720, 721-740, 741-760) (Chart 1)
5. Calculate the percentage of sample groups who fall in each range. For example,
in the Sampling Error Assignment Example in the 581-600 range we have two
groups or 2/56 or 3.57%. (Sheet 2)
6. Determine which sample groups, if randomly taken, would place you outside of
the range of 90 and 95 percent confident range. In our example our 95 percent
confidence range is 601-740 and our 90 percent confidence range is 621-740. So
if I had randomly chosen three students (Tim, Steve, and Alice) then I my sample
would fall out side of my 95 percent confidence level as shown as below. (Use
Sheet 3)
GMAT Scores
Number of Sample Groups
14
13
12
11
10
9
8
Tim, Steve,
& Alice
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
Ranges
7. It is important to note that the selection of Tim, Steve, and Alice is simply a rare
chance and not necessarily due to a mistake by those who collected the sample.
This chance is what we call a sample error.
Assignment:
1. Collect 8 names and GMAT Scores of random BYU MBA/Undergrad students
(you can make these up).
2. Using the above example, follow the exact same steps. You can use The Sample
Error Grid to save yourself a lot of time. All you have to do is simply change the
name and GMAT scores of the example and all of the individual sample groups
will automatically change.
3. Then after you have followed all of the above steps from the example, randomly
select 4 groups and see where they fall in the 90 and 95 percent confidence levels
you estimated by using sheet 2.
4. Finally, in your own words define Sample Error and how it can impact your
project.
**Hint**Do not just print off your entire Excel data! Show your names and GMAT
scores, your histogram, the percentages of sample groups that fall in each range,
whether your 4 chosen groups fall in or out of the 90% and 95% confidence intervals,
and make sure you define Sample Error and how it can impact your project.