Stat 101L – Exam 3
April 11, 2008
Name: ________________________
INSTRUCTIONS: Read the questions carefully and completely. Answer each question
and show work in the space provided. Partial credit will not be given if work is not
shown. When asked to explain, describe, or comment, do so within the context of the
problem. Be sure to include units when dealing with quantitative variables.
1. [15 pts] Short answer.
a) [2] Statistics is about … _______________. (Fill in the blank with one
word.)
b) [4] Give two ways you can decrease the width of a confidence interval and
explain why one way is better than the other.
c) [3] Explain what 95% confidence is without using the words confident,
chance, sure, or probability.
d) [3] Explain the relationship between the success/failure condition and the
confidence level.
e) [3] 25.3% of all undergraduate students enrolled at ISU are freshmen.
27.3% of all undergraduate students enrolled at ISU are in the College of
Liberal Arts and Sciences. 7.6% of all undergraduate students enrolled at
ISU are freshmen and in the College of Liberal Arts and Sciences. If a
student is selected at random from all students enrolled at ISU what is the
chance that student is a freshman or in the College of Liberal Arts and
Sciences?
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2. [15 pts] A study was done in Michigan with students in grades 4 – 6. The
students were asked the following question: What would you most like to do at
school? The choices were Make good grades, Be good at sports, or Be popular.
Students came from Rural, Suburban and Urban schools. Below are the data.
Rural
Suburban
Urban
Total
Make good
grades.
57
87
103
247
Be good
at sports.
50
42
49
141
Be popular.
Total
42
22
26
90
149
151
178
478
One student is selected at random from the 478.
a) [2] What is the probability the student selected is from a rural school?
b) [2] What is the probability the student selected wants to make good
grades?
c) [4] What is the probability the student selected wants to make good grades
given the student is from a rural school?
d) [3] Are being from a rural school and being from an urban school disjoint
events? Explain briefly.
e) [4] Are make good grades and rural school independent? Support your
answer with appropriate probability calculations.
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3. [15 pts] A CBS News poll conducted March 15-18, 2008 asked 1,067 randomly
selected U. S. adults the following question: “Looking back, do you think the
United States did the right thing in taking military action against Iraq, or
should the U.S. have stayed out?” Of the poll respondents: 384 answered “right
thing”, 630 answered “stayed out” and 53 were unsure.
a) [3] What is the population? Be specific.
b) [2] What is the sample? Be specific.
c) [6] Construct a 98% confidence interval on the population proportion that
thinks the United States did the right thing.
d) [4] Based on the confidence interval in c) does 50% of the population
think the United States did the right thing? Explain your answer briefly.
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4. [20 pts] People who work in smelting operations (where raw ore is turned into
metal) are exposed to strong electromagnetic fields. A study done in Norway
looked at the proportion of male births for women who worked in smelting
operations. In Norway as a whole 51.4% of all births are males. Of 204 women
randomly selected from all women who worked in smelting operations and who
gave birth to a baby, 92 gave birth to males. We are interested in seeing if the
proportion of male births for women in Norway who work in smelting operations
is less than that for all women in Norway. Note: The 10% condition is met.
a) [4] Set up the appropriate null and alternative hypotheses. Be sure to
define in words what the population proportion is.
b) [3] Verify that the success/failure condition for statistical inference is met.
c) [5] Compute the value of the test statistic and the associated P-value.
d) [2] Use the P-value to make a decision.
e) [3] State your conclusion within the context of the problem.
f) [3] Is the difference in the proportion of male births caused by the strong
electromagnetic fields? Explain briefly.
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5.
[10] We have 4 participants and we wish to assign 2 at random to a treatment
group and the other 2 to a control group. For each participant we could flip a fair
coin, if it turns up heads that participant goes to the control group, tails to the
treatment. However, this will not guarantee that there will be 2 in each group.
Therefore, once there are two participants in one group, the remaining participants
go to the other group without having to flip a coin.
a) [3] Complete the tree diagram below, C is for Control group and T is for
Treatment group, illustrating the random assignment of participants to
groups so there are 2 in each group.
Participant 1
Participant 2
Participant 3
Participant 4
Probability
C
T
b) [3] Use the fact that coin flips are independent and P(C) = P(T) = ½ to
compute the probability for each of the branches on the tree.
c) [4] Given your results in b), is this a good way to randomly assign
participants to treatment and control groups? Explain briefly.
I think I scored _________ out of 75 points on this exam.
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Formulas
Probability Rules:
Equally likely outcomes: Pr( Event ) =
# of outcomes in Event
total number of outcomes
Complements A and AC: P(AC) = 1 – P(A)
P(A or B) = P(A) + P(B) – P(A and B)
P(A and B) = P(A)*P(B|A)=P(B)*P(A|B)
A and B are disjoint if P(A and B) = 0
A and B are independent if P(A)=P(A|B) or P(B)=P(B|A)
Sampling Distribution of p̂ :
Mean: p
Standard Deviation: SD( pˆ ) =
p (1 − p )
n
z=
pˆ − p
p (1 − p )
n
Confidence interval for p:
pˆ − z *
pˆ (1 − pˆ )
pˆ (1 − pˆ )
to pˆ + z *
n
n
Confidence
z*
80%
1.282
90%
1.645
95%
2 or 1.96
98%
2.326
99%
2.576
Sample Size: (95% Confidence, conservative formula)
1
n=
(M.E.)2
Test Statistic:
H o : p = po
z=
pˆ − po
po (1 − po )
n
H A : p < po
P − value = Pr < z
H A : p > po
P − value = Pr > z
H A : p ≠ po
P − value = 2(Pr > z )
Table Z is on the back of this sheet.
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