Download Test 1 Review Packet

ECON 230
TEST 1 REVIEW SHEET
Practice problems
1. You’re interested in learning about how many different languages are spoken by LMU
students? To find the answer to this question you contact a random sample of 50 students in the
International Student Center.
a)
b)
c)
d)
e)
What is the population that is being discussed?
Is this the actual population that is being used to produce the sample? Explain.
What is the sample?
Does this sample represent the population well? Explain.
Can we generalize these results to all college students in the U.S.? Explain.
2. The ages of 10 U.S. Presidents (when they were elected) randomly chosen are as follows:
42 56 51 51 62 55 61 69 51 55
Find the mean, median, and mode for this set of data.
3. The frequency table below describes a sample of volunteers at a local hospital.
Age
Frequency (f)
15 - 29
21
30 - 44
16
45 - 59
23
60 - 74
18
75 - 89
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a) Construct a histogram for this set of data.
b) Based upon your histogram, make a reasonable estimate for the mean and standard
deviation.
c) Compute the sample mean.
d) Compute the sample standard deviation.
4. The following set of data represents the ages of men who won the Academy Award for
Best Actor from 1980 - 2003:
37 76 39 52 45 35 61 43 51 32 42 54
52 37 38 31 45 60 46 40 36 47 29 43
a) Construct a cumulative frequency distribution for this set of data using at least five classes.
b) Construct a histogram, labeling your data with the class midpoints.
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5. The mean time in a women’s 200-meter dash is 30.56 seconds with a standard deviation of 1.95
seconds. Apply Chebyshev’s Theorem to the data to find an interval that contains 84% of the
data.
6. What can be said about a set of data with a standard deviation of zero?
7. A department store sells sport shirts in three sizes (small, medium and large) and two sleeve
lengths (Full and Half).
Full Sleeve
Half Sleeve
Total
a)
b)
c)
d)
e)
f)
g)
Small
25
28
53
Medium
39
52
91
Large
56
30
86
Total
120
110
230
What is the probability that a shirt chosen from this group is a Large?
What is the probability that a shirt is Medium and has Full Sleeves?
What is the probability that a shirt is Small or has Half Sleeves?
What is the probability that a shirt is Large given that it has Half Sleeves?
What is the probability that a shirt is Half Sleeves given that it is a size Medium?
Are the events “Small size” and “Full Sleeves” mutually exclusive? Explain.
Are the events “Large size” and “Half Sleeves” independent? Explain. (Hint: You could use 2 of
your prior answers.)
8. From among ten of my students, I pick three at random to win three different prizes of $150, $75,
and $10. How many different possibilities are there for the three students that are picked to win
the different prizes?
9. Rita is playing 3 tennis matches.
a) List the sample space with the possible win and loss sequences that she can experience for this set
of three matches.
b) Is this an equally likely sample space? Explain.
10. A citizens action committee in California is comprised of six Democrats, eight Republicans, and
three Conservatives. If two different people are selected at random from this committee, find the
probability that they are both Democrats.
(CONTINUES ON NEXT PAGE)
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11. Suppose you know that people the Republicans have a 1/5 chance of approving of President
Obama’s performance. Everybody else has a 3/5 chance of approving of his performance.
Suppose that 1/3 of everybody is a Republican. If we pick out one person and that person
approves of Obama’s performance, what is the probability that person is a Republican?
(Hint: This problem is very similar to Problem 4.146 from the Chapter 4 problems)
12. Sixty-five percent of households in the United States subscribe to cable TV. If you randomly
select 5 households and ask each if they subscribe to cable TV, find the probability that
a) none of the houses has cable.
b) at least four houses have cable.
c) at most 2 houses have cable
(Hint: As part of your solution to part c), you need to find the probability that exactly
two of the houses have cable. To find this probability, be careful to account for all
of the different ways that exactly two houses can have cable)
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ECON 230
Test 1 Review Sheet/Answer Key
1. a) All LMU students
b) All LMU students are not being surveyed;
only students at the International Center are being considered. The actual population is students from the
International Center.
c) The 50 students from the International
Center who were surveyed.
d) Probably not, the International Center is
probably not a true cross-section of the
LMU student population.
e) This sample is from 1 college in CA; To
represent the whole college student
population in the country, more areas should be represented.
2.
Mean is 55.3.
Median is 55.
Mode is 51.
3a)
25
20
15
10
5
0
15 29
30 44
45 59
60 74
75 89
Class Boundaries
b) It should be something below the middle of the third class (52), since most of the data is in the lower groups.
Anything from 40-50 would be a reasonable guess.
c) 45.3
d) 17.7
4. a) Cumulative frequency distibution
Actor Ages
Midpoint
of each
class
29.5
39.5
49.5
59.5
69.5
79.5
frequency
Cumulative
frequency
3
10
8
2
0
1
3
13
21
23
23
24
Relative
frequency
0.125
0.417
0.333
0.083
0
0.0427
Cumulative
relative
frequency
0.125
0.542
0.875
0.958
0.958
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Also, make sure you know how to make percentage and cumulative percentage columns.
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b)
Histogram: Best Actors
12
10
8
6
4
2
0
29.5
39.5
49.5
59.5
69.5
79.5
Class Boundaries
5. At least 75% of the finishing times for the race will fall between 25.69 sec. and 35.43 sec.
6. All data values are the same
7. a)
b)
c)
d)
e)
f)
g)
86/230 = 0.3739
39/230 = 0.1696
53/230 + 110/230 – 28/230 = .5870
30/110 = 0.2727
52/91
No, 25 shirts are both.
Comparing answers (a) and (d), you can see P(Large) = 0.3739
 0.2727 P(Large | Half Sleeves).
8. 10*9*8 = 720
9. a)
b)
WWW,WWL,WLW,WLL
LWW,LWL,LLW, LLL
Maybe. Is she a 50/50 tennis player? Is she as likely to win as to lose?
10. (6/17)(5/16) = .11
11. To be discussed in class
12. To be discussed in class
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