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How Confident are you?
Math IV Unit 1 Test Review
1. In a large population of adults, the mean IQ is 115 with a standard deviation of 15.
Suppose 100 adults are randomly selected for a market research campaign. What is the
mean and the standard deviation of the sampling distribution of the sample mean?
 x    115 ;  x 

n
 1.5
2. Describe the CLT for means and the CLT for proportions.
CLT for means: shape of sampling distribution is approx.. Normal when n > 30
CLT for proportions: shape of sampling distribution is approx.. Normal when np > 10
AND n(1 – p) > 10
3. As the confidence level increases, the margin of error increases.
4. How does sample size affect the margin of error?
As sample size increases, margin of error decreases.
5. How does sample size affect the confidence interval?
As sample size increases, the width of the confidence interval decreases.
6. A random sample is to be chosen from a large population. If we want our margin of error
to be .8 and we know the standard deviation is 2.5, find how large a sample we would
need to be 95% confident.
A) 33
B) 34
C) 37
D) 38
E) 39
7. Consider the sampling distribution of sample means obtained by random sampling from
an infinite population. This population has a distribution that is highly skewed toward the
larger values.
a. How is the mean of the sampling distribution related to the mean of the
population?
The mean of the sampling distribution is equal to the population mean.
b. How is the standard deviation of the sampling distribution related to the standard
deviation of the population?
The standard deviation of the sampling distribution is smaller than the standard
deviation of the population.
c. How is the shape of the sampling distribution affected by the sample size?
As the sample size increases, the shape of the sampling distribution becomes
more Normal. (This is especially important considering that the shape of the
population is skewed.)
8. The mean weekly food budget of households in a certain community is $100 and the
standard deviation is $10.
a)
If one household is randomly selected, what is the probability that their
budget will be greater than $97?
P(X > 97) = .6179
b)
If a sample size of 100 is used, find the probability that the mean budget of
a sample is less than $95.
P( x < 95) = 0.000000287
* Go back and study Reese’s task and all worksheets.