Statistical Applications ACTIVITY 1: Establishing Teams: Reviewing and extending sampling
Why
You will be working with this team throughout the semester, so you need to begin getting to know your
teammates and working with them. Reviewing material on sampling (from your previous statistics course)
is necessary preparation for our work in the next week and provides a good focus for your first session. We
will be considering more precise and more powerful sampling methods – the first new tool is a more precise
estimator of a population standard deviation when sampling is from a finite population.
LEARNING OBJECTIVES
1. Work as a team, using the team roles
2. Recall basic sampling methods and concepts
3. Learn the use of the finite population correction factor in estimating standard deviation when sampling from a finite
population
CITERIA
1. Success in completing the exercises.
2. Success in working as a team
RESOURCES
1. Your Text, especially Chapter 7 and Sections 8.2 and 8.4
2. 40 minutes
PLAN
1. Select roles, if you have not already done so, and decide how you will carry out steps 2 and 3 (5 minutes)
2. Work through the exercises given here - be sure everyone understands all results (30 minutes)
3. Assess the team’s work and roles performances and prepare the Reflector’s and Recorder’s reports including team
grade (5 minutes).
4. Be prepared to discuss your results.
DISCUSSION
In your previous statistics course, you always worked with the assumption that that the selection of items in
a sample was independent – which is true if the population is infinite or sampling is done with replacement
[neither is very likely] and is “close enough for our calculations” if the sample is only a small part of the
population. The more precise methods used by professional polling organizations use the more accurate values
which correct for this lack of independence. We will use these more precise formulas during our work on this
section. For samples of size n, taken from a population of size N, the corrected formulas for σ¯xand σ¯pinvolve
a factor (the finite population correction factor)qN−n
N−1[shown in your text on p. 292]. In this case the error
allowance for a 1 −α% confidence interval for the population mean µis given by
E=tα/2qN−n
N−1
s
√n
and the error allowance for a 1 −α% confidence interval for the population proportion pis given by
E=zα/2qN−n
N−1q¯p(1−¯p)
n
These error allowances are smaller than those you saw before (since N−n
N−1is less than one)- reflecting the fact
that samples which are a larger part of the population vary less than those which are a smaller part. If we know
the population size we can give estimates that are more precise (less allowance for error needed) – naturally
the polling organizations prefer this.
EXERCISE
1. Information on team members. For each member:
(a) Name
(b) Hometown – How long have you lived there?
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