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Stats 5 Day 3
Agenda
Homework Due Monday 3/7:
• Chapter 18 p. 428 #7, 9, 10, 11, 15, 18,
23, 25
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Objective: SWBAT solve sampling distribution
model problems for proportions (%s) and means
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Agenda:
Last Week
Sampling Distribution Models!
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We saw that when a distribution of
samples are taken they create a normal
curve
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We noted the 3 conditions for the sample:
random, np and nq> 10, 10% condition
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We reviewed using the normal model to
find probabilities
Sampling
Distributions
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As we saw last week…

NORMAL
Samples can be modeled by a _____curve

Samples that meet the 3 conditions
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
RANDOM
Samples must be _____________
np and nq > 10
_____
10%
______% condition: the sample must not be
POPULATION
larger than 10%
______ of the ______________
will fall on a normal curve

The more samples, the less
Sample Variability
Sample Proportion
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What is a proportion?
⌃
Sample proportion = p* or p
• number of successes in a sample/
total observations
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Population proportion = number of
successes/ total population
Mean and SD of
Sample Proportions
The mean, as more samples are added giving
less variability, then becomes p, population
proportion
We know the standard deviation for the
number of successes is √npq
• and now we want the standard deviation of
the proportion of successes (or standard
variation or standard error) so
• √npq / n = √(pq/n)
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Consider This…
Of all cars on the interstate, 80%
speed. What proportion of speeders
might we see among the next 50
cars? (that is, draw a normal curve
and describe the 68-95-99.7
proportions)
• **be sure to check conditions first!
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Consider This…
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According to the US News and World
Report, in the population of 4,361
students enrolled in Penn State
bachelor’s degree programs, 811 have
military experience, so p=811/4361 =
18.6%. If we were to randomly select
75 students to participate in a research
study, what is the probability that more
than 25% have military experience?
Consider this…
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Suppose 60% of all voters in Cook County
intend to vote for Clinton in the upcoming
election. A poll is taken, 100 voters are
selected by SRS. Let p* be the proportion of
sampled voters who intend to vote for
Clinton. Draw the Sampling Distribution
Model. What is the probability of p*<0.5?
(That is, what is the probability less than half
of the sampled voters intend to vote for
Clinton? This may lead to an incorrect
prediction of Clinton losing.)
Another Example
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According to a Gallup Poll in 2006,
44% of American households own a
dog. What is the probability that a
random sample of 60 households will
have a sample proportion greater
than 40%?
Exit Ticket
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When done you may start hw