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Collect 9.1 Coop. Asmnt. &…
9.10
____________ bias and _______________ variability
____________ bias and _______________ variability
____________ bias and _______________ variability
____________ bias and _______________ variability
9.2 Sample Proportions
Consider this…
A polling organization asks a SRS of 1500
first-year college students whether they
applied for admission to any other college. In
fact, 35% of all first-year students applied to
colleges besides the one they are attending.
What is the probability that the random
sample of 1500 students will give a result
within 2 percentage points of this true value?
• What do you need to know in order to
answer this question?
Sampling Distributions Activity
• Rice University Sampling Distribution Applet
– Choose a couple of different sample sizes
• Note: the mean and standard deviation for the
sampling distribution are algebraically derived
from what we know about the mean and standard
deviation of a binomial random variable.
• P-hat = (Count of “successes” in
sample)/(size of sample) = X/n
More formulas and
their construction
“Rule of Thumb 2” gives exactly the same conditions
for using a Normal approximation to the sampling
distribution of p-hat as for a Normal approximation to
the binomial. This should not be a surprise as
proportions are just another way to look at counts.
Let’s work through
Example 9.7
P 584
Step 1:
Step 2:
Step 3:
WORD CHOICE: “We see that almost 90% of all samples will give a result
within 2 percentage points of the truth of the population” (p 585).
Ex 9.8
P 586
Step 1:
Step 2:
Step 3:
Fig 9.14
Another example
• Suppose a student taking a 100 question
multiple choice final (with 5 possible
answers each). This student didn’t study and
must guess on every question. What is the
probability that this student will get at least
30% right on the test?
How can we do this as a binomial?
Context: 100 questions, 5 possible answers each,
want to score at least 30%.
P(X > 30) =
= 1-binomcdf(100,.2,29) =
How do the two computational methods compare?
Practice: 9.20 & 9.22
Homework: 9.25, 9.27, 9.30
Tomorrow:
Q&A
9.2 Coop Asmnt