Math 1070-003
Exam 3 Review
15 April 2013
The following questions are designed to help you prepare for Exam 3. You
should also study the relevant vocabulary, concepts, and formulas. You will
be allowed one 8.5 × 5.5 sheet of paper (half of a letter-size sheet of paper)
in the exam. The relevant tables will be provided for you.
For each question, determine which procedures to use, and then carry out the hypothesis
test or find the confidence interval.
1. A researcher believes that the weights (in grams) of adult males in two species of beetles
follow the Normal distribution. He takes an SRS of each species and calculates the
following information:
Group n x
s
A
31 15 4.61
B
17 21 7.34
Is there strong evidence (at the level α = 0.10) that species B is larger than species A,
on average?
2. Many years of data support the assumption that the lifetimes of bald eagles are Normally
Distributed with mean 37 years and standard deviation 6 years. Rachel Carson finds
that an SRS of 9 bald eagles in agricultural areas with long-term heavy DDT use have
an average lifespan of 15 years. Is there sufficient evidence, at the level α = 0.10 that
DDT causes bald eagles to die prematurely? Find a 99% confidence interval for the
lifespan of bald eagles in the presence of DDT.
3. Some people claim that eating meat causes higher cancer rates. In the general population, 8.70% of adults ages 40-60 are diagnosed with some form of cancer. Let’s say
that the cancer rate in a simple random sample of 300 adults ages 40-60 who eat meat
is 8.92%. Is this difference significant at the level α = 0.05? (In other words, is there
sufficient evidence to conclude that the proportion of meat-eaters who are diagnosed
with cancer is higher than the proportion in the general population?)
4. Researchers want to determine whether children with obese parents are more likely to
be obese. In a matched-pairs study, 10 single-child two-parent families with two obese
parents were matched with similar families with two non-obese parents. The average
difference between the children’s body mass indexes (obese parents minus non-obese
parents) was 1.25 with sample standard deviation 0.97. Is there significant evidence (at
the level α = 0.01) that children with obese parents are more likely to be obese?
5. The National Longitudinal Study of Adolescent Health interviewed several thousand
teens (grades 7 to 12). One question asked was “What do you think are the chances
that you will be married in the next ten years?” Here is a table of the responses by
gender:
Female
Almost no chance
119
150
Some chance, but probably not
A 50-50 chance
447
735
A good chance
Almost certain
1174
Male
103
171
512
710
756
Is there evidence of a difference between male and female teenagers in their distributions
of opinions about marriage?
6. Give an example of a Type I error.
7. Give an example of a Type II error.
8. Assuming that the null hypothesis (H0 : µ = µ0 ) is true, what distribution do each of
the following statistics have? (Assume a random sample of size n, with σ, µ0 , x, s, etc
as usual.)
x − µ0
(a) z = σ √
/ n
x − µ0
(b) t = s √
/ n
p̂ − p0
(c) z = q
p̂(1−p̂)
n
9. What is the relationship between the margin of error of a 99% confidence interval and
the margin of error of a 90% confidence interval, calculated from the same data?
10. Suppose that Alice and Bob are researchers studying the same variable in the same
population. They find the same sample mean and sample standard deviation and are
testing the same hypotheses, but Alice’s study has a larger sample size than Bob’s. What
can you say about the P -value of Alice’s hypothesis test in relation to Bob’s?
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