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Session Review
Statistics 226
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
Luyun
Stat 226
Anna Peterson
3/2/16
Steps for solving sampling distribution problems
Step 1: Read the problem and note all the information given.
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Step 2: identify if the question is asking for a probability associated with one observation (n=1)
or the mean of a set of observations.
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If n=1 (individual observation)
o
o
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If n>1 (mean of a set of n observations)
o
o
o
Why do we use the sample mean x¯ to estimate the unknown population mean µ?
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The sample mean will vary _______ less than individual observation.
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New York stock exchange. Suppose that the percentage returns for a given of stocks listed on the
New York Stock Exchange follow a distribution that is skewed with mean µ = 10.5 percent and
standard deviation σ = 8 percent. From this distribution, suppose you obtain a random sample of
size 64.
(a) What is the shape of the sampling distribution of the sample mean?
Circle one: Approximate to Normal
or
Not Normal
(b) Find the mean and the standard deviation of the sampling distribution of the sample
mean.
Center (mean): __________
Spread (standard deviation): ____________
(c) Can you find the probability that a single stock will have more than a 12 percent return in
a given year? If yes, what is the probability? If no, explain why not?
(d) Can you find the probability that a sample mean (of size 64) will have more than a 12
percent return in a given year? If yes, what is the probability? If no, explain why not.
(e) Can you find the 5th percentile of the sampling distribution of the sample mean x¯? if yes,
compute it, if no, explain why not.
The number of Nestle chocolate chips in a bag follows a non-normal distribution with a mean of
360 chocolate chips and a standard deviation of 24 chocolate chips. To conduct a sample of their
claim, I randomly choose 45 bags and conduct the number of chocolate chips in each bag.
(a)
What is the distribution of the number of chocolate chips in any given bags? Make sure
to specify the mean and standard deviation in addition to the distribution name (if known)
(b) What is the distribution of the mean number of chocolate chips in a bag based on
samples of 45 bags? Justify your answer.
(c) What is the probability that the mean number of chocolate chips in a bad in a sample of
45 bags is smaller than 340?
(d) If I was interested in sample of 90 bags, how would the probability in the above problem
change? (No need to calculate, just say what would happen with a justification).
(e)
What is the probability that the mean number of chocolate chips in a bag in a sample of
45 bags is between 345 and 352?