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Topic: Test #6
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Al Coons

Posts: 898
Registered: 12/4/04
Test #6
Posted: Mar 2, 1997 8:15 PM
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Please feel free to use any part of this and even freer to email me back with
suggestions and misconceptions I have imposed on my students. This test went
well but not as well as previous tests. I noticed that my students did not
do as good a job intrepreting the results of tests as they have in the past.
In addition, they did not pick up the need to interpet confidence intervals
as providing information about magnitudes in addition to duality with tests
of significance.

2/26/97 AP Statistics-Test 6: WS Activity 21-25; BPS 6.1, 2, 7.2

1. Circle the correct answer: A confidence interval is robust when:

a) Changes in the confidence level do not affect the confidence interval
very much.
b) The confidence interval does not change if the assumptions of the
procedure are violated.
c) The confidence interval does not change very much if the assumptions of
the procedure are violated.
d) The confidence interval is large.

2. Circle the correct answer: The data in a two-sided two-proportion test
of significance produces a statistically significant result. Then a 95%
confidence interval is computed.

a) About 95% of the data should be contained in the interval.
b) About 95% of the time we expect the true population proportion to be in
the interval.
c) Zero is not in the interval.
d) Zero is in the interval.
e) None of the above.

3. Demonstrate your knowledge of the meaning of Standard Error in explaining
whether standard error or standard deviation is used in doing inference for a
mean of a population after gathering a sample from an unknown population.

4. Explain why you would be very concerned about a study which reported
statistically significant results (p = 0.001, df = 0) after doing a
one-sample t-test for the mean of a population. Be specific.

5. Explain why it is necessary to have the t-distributions?

6. A student searched the Internet for data for a project. He found a file
with the population of each of the states of the USA. He used his calculator
to construct a 95% confidence interval about the mean of the populations.
Given the data, why does this not make sense?

7. Explain why the pooled proportion, p(c), is used in a two-proportion
test of significance but is not used in calculating the corresponding
confidence interval.

8. An experiment is performed in which the proportion of males in AP
Statistics Classes is compared to the proportion of males in AP Calculus
classes. A two-sided two-proportion test of significance is performed with
Ho: Theta(Stats) = Theta(calc). The test produces a statistically
significant result with a confidence interval of (-0.3, -0.1) where t =
(p-hat(stats)-p-hat(calc))/root[(p-hat(c))(1- p-hat(c))(1/n1+1/n2)]

What additional information not already stated above is provided by the
confidence interval? Your answer should be as specific as possible.

9. The weight of 9 men have mean 175 lbs. and standard deviation 15 lbs.
Calculate the standard error of the mean.

10. It is logical to assume that a dirty air filter will reduce the gas
mileage of a car. In an experiment 6 pairs of identical cars are rented. In
one car of each pair a brand NEW air filter is installed. On the other car
of each pair a DIRTY air filter (of the same type) is installed. Gas mileage
for these cars during the experiment is listed below:

Pairs Gas Mileage with Clean Filter Gas Mileage with Dirty Filter
Small Chevys 23 21
Medium Chevys 22 20
Large Chevys 19 17
Small Fords 25 26
Medium Fords 25 21
Large Fords 25 23

a) What is the name of the most appropriate test of significance to apply to
see if dirty air filters reduce the gas mileage of a sensible population of

b) While supplying just enough information to keep your teacher informed of
what you are doing, use your calculator to perform the computations involved
in the test you just mentioned. Include at some point the formula for the
test statistic.

c) Carefully and fully report the results of the test in a meaningful way.

11. Cuckoos lay their eggs in the nests of other birds. Some biologists
speculate that the size of the cuckoo's eggs might be different depending on
whether the eggs are laid in warbler's nests or wren's nests. To check this,
biologist searched a wildlife refuge for warblers' and wrens' nests. Summary
statistics for the lengths (in mm) of cuckoo's eggs found in the nest of
warblers and wrens are shown below:

From Warblers' nests: n1 = 29, x-bar=21.62, s1= 0.65
From Wren's nests: n2 =35, x-bar = 21.12, s2=0.75

a. Demonstrate you can do the following BY HAND and with tables:

Do a fully annotated test of significance to determine if the biologists'
speculation that the size of the eggs differ depending on whether they are
laid in warblers' nest or wrens' nests.

b. Demonstrate you can do the following BY HAND and with tables:

Determine and fully interpret a 96% confidence interval for the above


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