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Session Review
Statistics 226
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
Luyun
Stat 226
Anna Peterson
2/27/16
Self Quiz:
1.) The Central Limit Theorem says that the sampling distribution of the sample mean is
approximately normal if…
a. All possible samples are selected
b. The sample size is large
c. The standard error of the sampling distribution is small
2.) The Central Limit Theorem says that the mean of the sampling distribution of the sample means
is…
a. Equal to the population mean divided by the square root of the sample size
b. Close to the population mean if the sample size is large
c. Exactly equal to the population mean
3.) The Central Limit Theorem says that the standard deviation of the sampling distribution of the
sample mean is…
a. Equal to the population standard deviation divided by the square root of the sample size
b. Close to the population standard deviation if the sample size is large
c. Exactly equal to the standard deviation of the population distribution
4.) Samples of size 25 are selected from a population with mean 40 and standard deviation 7.5.
The mean of the sampling distribution of sample means is…
a. 7.5
b. 8
c. 40
5.) Samples of size 25 are selected from a population with mean 40 and standard deviation 7.5.
The standard error of the sampling distribution of sample means is…
a. 0.3
b. 1.5
c. 7.5
What does Central Limit Theorem tell us about the sampling distribution of the sample mean?
How do you apply Central Limit Theorem?
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Suppose that we randomly select a sample of 64 measurements from a population having a mean
equal to 20 and a standard deviation equal to 4.
(a) Describe the shape of the sampling distribution of the sample mean. Do we need to make
any assumptions about the shape of the population? Why or why not?
(b) Find the mean and the standard deviation of the sampling distribution of the sample
mean.
(c) Can you find the probability that a single measurement will be greater than 21? If so,
what is the probability?
(d) Calculate the probability that we will obtain a sample mean greater than 21.
The average length of a hospital in the US is μ=9 days with standard deviation of σ=30 days.
Assume a simple random sample of 100 patients is obtained and the mean stay for 100
patients is obtained. What is the probability that the average length of stay for this group of
patients will be less than 9.6 days? To answer this question, we usually think of the following
steps:
(a) What is the mean of the sampling distribution of x̅ for samples of size 100
(b) What is the standard deviation of the sampling distribution of x̅ for sample size 100
(c) What is the probability to obtain a sample mean less than 9.6 days?
The number of accidents of week at a hazardous intersection varies with mean μ=2.2 and
standard deviation σ=1.4. This is distribution only takes whole-number values, so it is
certainly not Normal.
(a) Let x̅ be the mean number of accidents per week at the intersection during a year (52
weeks). What is the approximate distribution of x̅ according to the Central Limit
Theorem?
(b) What is the approximate probability that x̅ is less than 2?
(c) What is the approximate probability that there are fewer than 100 accidents at the
intersection in a year?