# Notes on 6-9

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Sampling Distributions

Properties of a sampling distribution of
means:
Sampling Distributions

Properties of a sampling distribution of
proportions:
About 13% of the population is left-handed. What’s the
probability that less than 10% of a class of 50 is left-handed?
The mean adult weight is 175 pounds with a standard deviation of
25 pounds. Assumption of normal is appropriate. What is the
probability that I randomly choose a person who is more than 200
pounds?
The mean adult weight is 175 pounds with a standard
deviation of 25 pounds. The weight limit of an elevator is an
average of 200 pounds per person. Max is 2000 pounds.
What’s the probability that 10 people get on the elevator
overload its weight limit? Assume normal distribution.
The mean score on a standardized test is 120 with a
standard deviation of 15 points. What’s the probability that a
group of 40 people will have a mean score of at least 128.
Approximately 28% of the population would like a new house.
What’s the probability that at most 40 out of 150 people interviewed
will want a new house.
In May 2002, the Gallup Poll asked 537 randomly sampled adults
the question, “Do you believe the death penalty is applied fairly or
unfairly in this country today”. Of these, 53% said “fairly”. Find a
90% confidence interval for the proportion of US adults who agree.
A survey of 2500 golfers showed that 280 of them are
left handed. Construct a 92% confidence interval to
estimate the proportion of left handed golfers.
What happens to the interval if I go from a 92% confidence
interval to a 99% interval using the same sample size?
If I keep the same confidence level (92%), but increase the
sample size by 100, what will happen to the interval?
Explain what a 90% confidence interval is.
Explain what a 90% confidence level is.
Sample Size
Standard Error


It’s the estimated standard deviation of the
statistic
E  z
2
pq
n
An article by the right to die organization gave a proportion of
physician’s who agree with their cause. I want to test their claim.
I want to be within 0.05 with 95% confidence, how many must I
sample? (Assume p = 0.5)
Why did I let p = 0.5? If proportion is not given, use p =
0.5 because it’s including the most error. (Let n = 100)
p
q
0.1
0.9
0.2
0.8
0.3
0.7
0.4
0.6
0.5
0.5
pq
n
A pollster wishes to estimate the proportion of U.S. voters who
favor capital punishment. How large a sample is needed in order
to be 95% confident that the sample proportion will not differ from
the true proportion by more than 2%?
An article by the right to die organization gave a proportion of
physician’s who agree with their cause. I want to test their claim.
I want to be within 0.05 with 95% confidence, how many must I
sample?
A pollster wishes to estimate the proportion of U.S. voters
who favor capital punishment. How large a sample is needed
in order to be 95% confident that the sample proportion will
not differ from the true proportion by more than 2%?
Find the minimum required sample size if you want to be 95%
confident that the sample mean is within 2 units of the population
mean if the population standard deviation is 4.8.
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Worksheet
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