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Statistics (I)
2011Fal
Quiz #1
Date: 10/13/2011
A.
MULTIPLE CHOICE QUESTIONS (30%)
1.
Temperature is an example of a variable that uses
a.
the ratio scale
b. the interval scale
c.
the ordinal scale
d. either the ratio or the ordinal scale
2.
The nominal scale of measurement has the properties of the
a.
ordinal scale
b.
only interval scale
c.
ratio scale
d.
None of these alternatives is correct.
3.
Statistical studies in which researchers control variables of interest are
a.
experimental studies
b.
control observational studies
c.
non-experimental studies
d.
observational studies
4.
A statistics professor asked students in a class their ages. On the basis of this information, the
professor states that the average age of all the students in the university is 24 years. This is an
example of
a.
a census
b.
descriptive statistics
c.
an experiment
d.
statistical inference
5.
Qualitative data can be graphically represented by using a(n)
a.
histogram
b. frequency polygon
c.
ogive
d. bar graph
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6.
7.
Since the population size is always larger than the sample size, then the sample statistic
a.
can never be larger than the population parameter
b.
c.
d.
can never be equal to the population parameter
can be smaller, larger, or equal to the population parameter
can never be smaller than the population parameter
The value which has half of the observations above it and half the observations below it is
called the
a.
b.
c.
range
median
mean
d.
mode
8.
When data are positively skewed, the mean will usually be
a.
greater than the median
b.
smaller than the median
c.
equal to the median
d.
positive
9.
The numerical value of the standard deviation can never be
a.
larger than the variance
b.
zero
c.
negative
d.
smaller than the variance
10. The value of the sum of the deviations from the mean, i.e., ( x  x) must always be
a.
b.
c.
d.
less than the zero
negative
either positive or negative depending on whether the mean is negative or positive
zero
11. If the coefficient of variation is 40% and the mean is 70, then the variance is
a.
b.
c.
d.
28
2800
1.75
784
2
12. If a six sided die is tossed two times and “3” shows up both times, the probability of “3” on the
third trial is
a.
much larger than any other outcome
b.
c.
d.
much smaller than any other outcome
1/6
1/216
13. If P(A) = 0.4, P(B| A) = 0.35, P(A  B) =0.69, then P(B) =
a. 0.14
b. 0.43
c. 0.75
d. 0.59
14. Two events with nonzero probabilities
a. can be both mutually exclusive and independent
b. can not be both mutually exclusive and independent
c. are always mutually exclusive
d. are always independent
15. If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then
P(AB) =
a. 0.05
b. 0.0325
c. 0.65
d. 0.8
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B.
Problems (70%)
1.
(8%) A sample of twelve families was taken. Each family was asked how many times per
week they dine in restaurants.
2
1
0
2
0
2
1
Their responses are given below.
2
0
2
1 2
Using this data set, compute the
a. mode
b. median
c. mean
d. range
e. interquartile range
f. variance
g. standard deviation
h. coefficient of variation
2.
(8%) The following data represent the daily supply (y in thousands of units) and the unit
price (x in dollars) for a product.
Daily Supply (y) Unit Price (x)
5
2
7
4
9
8
12
5
10
13
16
16
a.
b.
c.
d.
7
8
16
6
Compute and interpret the sample covariance for the above data.
Compute the standard deviation for the daily supply.
Compute the standard deviation for the unit price.
Compute and interpret the sample correlation coefficient.
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3. (8%) As a company manager for Claimstat Corporation there is a 0.40 probability that you will
be promoted this year. There is a 0.72 probability that you will get a promotion or a raise.
The probability of getting a promotion and a raise is 0.25.
a. If you get a promotion, what is the probability that you will also get a raise?
b. Are getting a raise and being promoted independent events? Explain using
probabilities.
c. Are these two events mutually exclusive? Explain using probabilities.
d. Are these two events independent? Explain using probabilities.
4.
(6%) Assume two events A and B are mutually exclusive and, furthermore, P(A) = 0.2 and
P(B) = 0.4.
a. Find P(A  B).
b. Find P(A  B).
c. Find P(AB).
5.
(14%) A small town has 5,600 residents. The residents in the town were asked whether or not
they favored building a new bridge across the river. You are given the following information
on the residents' responses, broken down by sex.
In Favor
Opposed
Total
a.
b.
c.
d.
e.
f.
g.
Men
1,400
840
2,240
Women
280
3,080
3,360
Total
1,680
3,920
5,600
Find the joint probability table.
Find the marginal probabilities.
What is the probability that a randomly selected resident is a man and is in favor of
building the bridge?
What is the probability that a randomly selected resident is a man?
What is the probability that a randomly selected resident is in favor of building the bridge?
What is the probability that a randomly selected resident is a man or in favor of building
the bridge?
A randomly selected resident turns out to be male. Compute the probability that he is in
favor of building the bridge.
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6.
(8%) In a recent survey about appliance ownership, 58.3% of the respondents indicated that
they own Maytag appliances, while 23.9% indicated they own both Maytag and GE appliances
and 70.7% said they own at least one of the two appliances.
Define the events as
M = Owning a Maytag appliance
G = Owning a GE appliance
a.
b.
c.
What is the probability that a respondent owns a GE appliance?
Given that a respondent owns a Maytag appliance, what is the probability that the
respondent also owns a GE appliance?
Are events “M” and “G” mutually exclusive? Why or why not? Explain, using
d.
probabilities.
Are the two events “M” and “G” independent?
Explain, using probabilities.
7. (6%) What is the probability of drawing the 4 aces as the first 4 cards if 4 cards are drawn at
random and without replacement from a deck of 52 playing cards? Please note that you are
required to use conditional probability instead of counting rule.
8. (6%) In a factory of 4 machines producing the same product. Machine A, B, C, and D produces
10%, 20%, 30%, and 40% of products, respectively. The proportion of defective items produced
by these machines follows 0.001 for machine A, 0.0005 for machine B, 0.005 for machine C,
0.002 for machine D. An item randomly selected is found to be defective. What is the
probability that the item was produced by A? C?
9. (6%) The circuit shown below operates only if there is a path of functional devices from left to
right. The probability that each device functions is shown on the graph. Assume that devices fail
independently. What is the probability that the circuit operates?
6
0.9
0.95
0.9
0.99
0.95
0.9
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