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Sta220 - Statistics
Mr. Smith
Room 310
Class #15
Section 4.9
We are interested in making an inference about
the mean 𝜇 of some population.
Why?
- Estimate the mean useful life of automobiles
- Mean number of crimes per month in a large
city
- Mean yield per acre of new soybean hybrid
Definition
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What about the shape of the sampling
distribution?
Two theorems provide this information.
Theorem
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Theorem
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The Central Limit Theorem is so powerful
because now we no longer need to know the
distribution of the population. The Central Limit
Theorem applies to all types of population
distributions.
Figure 4.39
Sampling
distributions
of x for
different
populations
and different
sample sizes
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reserved.
Problem 4.29
Suppose we have selected a random sample of n =
36 observation from a population with mean equal
to 80 and standard deviation equal to 6. It is known
that the population is not extremely skewed.
a) Sketch the relative frequency distributions for
the population and for the sampling distribution
of the sample mean 𝑥.
b) Find the probability that 𝑥 will be larger than 82
Figure 4.40A population relative frequency
distribution and the sampling distribution for x
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b.
Figure 4.41 The sampling distribution for
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x
Problem 4.30
A manufacturer of automobile batteries claims that the
distribution of the lengths of life and its best battery has a mean
of 54 months and a standard deviation of 6 months. Suppose a
consumer group decides to check the claim by purchasing a
sample of 50 of the batteries and subjecting them to tests that
estimate the battery’s life.
a) Assuming that the manufacturer’s claim is true, describe the
sampling distribution of the mean lifetime of a sample of 50
batteries.
b) Assuming that the manufacturer’s claim is true, what is the
probability that the consumer group’s sample has a mean life
of fewer 52 months?
Figure 4.42 The sampling distribution of
Example 6.8 for n = 50
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reserved.
x in
Homework 4.8 and 4.9 due by Wednesday
Quiz Chapter 4 and CH. 4 Homework Review due by
Wednesday
Test on Chapter 4 Thursday, Review will be passed
out tomorrow.
Chapter 5 will start Friday