12 Total Points
NOTE: All questions are worth 1 point, unless otherwise noted.
Homework 5
Reading Questions
In this module we will examine the different sampling methods. We will see how the method of sampling
impacts the estimates one obtains from a sample of data. In particular we will examine two properties that
are desirable: unbiasedness and precision.
Answer the following questions regarding the “readings”:
1.
How does random sampling provide samples that are representative of the population they are
drawn from?
Random sampling produces representative samples of the population by eliminating voluntary
response bias and protecting against undercoverage bias. Every unit in the population has the same
chance of being selected. However, even when random sampling is used, you don’t expect the estimate
from each individual sample to match the population average exactly.
2.
What type of survey bias does random sampling NOT reduce?
Random sampling does NOT reduce response bias. Response bias occurs when there is a problem in
measurement process of survey research. Examples of response bias are leading questions (wording
of the question may favor one response or another) and social desirability (responses are biased due
to what participants believe is socially desirable, especially when results are not confidential).
3.
What type of survey bias can a convenience sample sometimes cause?
A convenience sample can sometimes cause undercoverage bias. Undercoverage occurs when some
members of the population are inadequately represented in the sample.
4.
How do you know when a sample statistic is unbiased?
Unbiasedness indicates that the estimation method used produces a distribution of the estimated
parameter that is neither too large nor too small. Therefore in order to determine if a sample statistic
is unbiased, you must study the distribution of estimates. If the statistic is unbiased, the average of all
the statistics from all possible samples will equal the true population parameter, or summary measure
of the population. If the sampling method produces characteristics of the sample that are significantly
different than those characteristics of the population, then the sampling method is biased.
5.
Does increasing the sample size reduce sampling error? Explain.
Yes, increasing the sample size will reduce the sampling error. Sampling error is the difference
between the sample value and the population value. If the sample size increases, then the sample
value will be closer to the population value, which in turn will reduce the sampling error.
6.
Does increasing the sample size reduce survey bias? Explain.
CATALST Project
1
12 Total Points
No, increasing the sample size will not necessarily reduce survey bias. A larger sample size will not
remedy the problems that are based on the methods of the actual testing.
7. The standard error is a measure of the precision of the sample mean.
8. How does sample size affect the margin of error?
Larger samples sizes will reduce the margin of error. As sample sizes increase the maximum margin
of error percentage will decrease.
Write a report that answers the research question “What is the average word length in the
Gettysburg address?” (4pts).
The report should include:
– how the interval was computed,
– what the interval is,
– an interpretation of the interval and
– appropriate conclusions based on the interval and study design.
The average word length in the Gettysburg address is between 3.46 and 5.14 letters with a confidence
interval of 95% (mean +/- 2SE). When looking at 2 standard errors of the mean from the mean, 95% of
the distribution is covered – resulting in a 95% confidence interval. This interval was computed by
looking at the average word length from the samples chosen - the mean was 4.30. The standard error of
the mean was .42 with a margin of error of .84 (2 x .42). By looking at values within .84 points from the
mean we have any values from 3.46 (4.30-.84) and 5.14 (4.30+.84). Based on this interval, we can be
confident that the true parameter is any value between 3.46 and 5.14; any value within that range would
be a good estimate. We can conclude that these results are unbiased because the sample mean (4.30)
matches the population mean.
9.
CATALST Project
2