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Posted: January 13th, 2023
What is the special name for the standard deviation of a sampling distribution
Instructions:
If you missed 5 points (not five questions!) or fewer, you need only answer the
questions you missed and complete problem 11 (which was originally extra
credit). If you missed more than 5 points, you should re-do the entire test.
You will receive 5 points for corrections which will be added to your test
scores after the final exam. Your total score may not exceed 100%.
DUE DATE:
May 6, 5:30 PM
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1.
What
is a sampling distribution?
2.
What
is the special name for the standard deviation of a sampling distribution?____________________
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3.
For
a sampling distribution of the proportion
from a population with population proportion p,
What is the
mean of the distribution? What is the
standard error of the distribution?
4.
For
a sampling distribution of the mean
from a population with population mean.gif">
and standard deviation.gif">,
What is the
mean of the distribution?
What is the standard error of the distribution?
5.
How
do you determine (theoretically, without simulation) if the sampling
distribution of a sample proportion is likely to be approximately Normal?
6.
We
usually assume that the sampling distribution of the sample mean is
approximately Normal if the sample size is at least 30.
Under what conditions would we be safe in
assuming Normality for a smaller sample size?
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Under what conditions might we need a larger
sample size?
7.
You
showed by simulation that the standard
error of a sampling distribution would decrease
if you increased the sample size. Show how the formula for the standard error
can be used to confirm this theoretically.
8.
By
what factor would you have to increase the sample size to cut the standard
error in half? Provide evidence for your answer. You may use empirical evidence from your lab
or theoretical evidence by using the formula, as we did in class.
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9.
When
using the StatKey applets, you can change two numbers:
the
sample SIZE OR the NUMBER of samples
You
increase one of them to try to produce a better approximation to the true
sampling distribution and a better estimate of the true standard error. Which one? __________________
You increase the other to produce an entirely different sampling distribution
with a different (smaller) standard error.
Which one? ___________________________
10. During
the 2008 presidential election, newspapers reported that Barak Obama received
40% of the white male vote. If this is true, what is the probability
that a random sample of 1000 white male voters had a sample percentage of more
than 42% voting for Mr. Obama? Show
all the steps for using the Normal model to answer this question. (a) First
verify that the Normal model is appropriate.
(b) Find the standard error. (c) Find the Z-score and interpret it. (d)Then find the probability an applet. Make a sketch of the distribution you used. Shade the area representing the probability
you found.
.jpg">
11.A
sampling distribution is shown for the proportion of US citizens over 15 years
old who have never been married, using the data from the 2010 US Census and
random samples of size n = 500.
a).
What does one dot in the dotplot represent?
b) Use the sampling distribution to
estimate the proportion p
of all US citizens over 15 years old who have never been married.
__________________
c)
Verify using the formula that the sampling distribution is approximately
Normal.
d) From the dotplot, it appears that it
would be quite unlikely to obtain a sample of size 500 from this population
with a sample proportion of 0.27 or less. Verify this theoretically by assuming
that the sampling distribution is approximately Normal (as you showed in part
c) and finding the probability of obtaining such a sample Show all your work. If you used an applet,
make a sketch.
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