Download File - Elisha Kostka

Elisha Mae Kostka
Assignment Mock Test 1 due 02/11/2015 at 09:01am PST
243
• A
• A
• B
1. (1 pt) Luis Gonzalez began his career as a major league
baseball player in 1990. You are given a sample of the number
of homeruns hit in 5 of the seasons.
4. (1 pt)
Of the variables you have studied so far, which type yields nonnumerical data?
• A. Quantitative discrete
• B. Quantitative continuous
• C. Qualitative
• D. None of the above
What type of study is this?
• A. DESCRIPTIVE
• B. INFERENTIAL
Correct Answers:
• B
2. (1 pt) Annual tuition rates are a concern for the majority
of college students at public universities. Suppose you are provided with the resident annual tuition (for 15 credit hours) for
each public university in the U.S. for the 2003-2004 school year.
Correct Answers:
• C
5. (1 pt)
a - Qualitative data
b - Discrete, quantitative data
c - Continuous, quantitative data
What type of study is this?
• A. DESCRIPTIVE
• B. INFERENTIAL
Fill in the appropriate letter (from above) of the term defined
in each of the parts below.
Correct Answers:
• A
a) Data obtained by observing numerical values which form
some interval of numbers
answer:
b) Data obtained from a nonnumerically valued variable
answer:
c) Data obtained by observing numerical values which form
a finite, or countably infinite, set of numbers
answer:
3. (1 pt) A sample of 30 dentists from Seattle is taken to
estimate the median income of all Seattle residents.
Is this study
• A. REPRESENTATIVE?
• B. NON-REPRESENTATIVE?
A simple random sample of men over age 18 is taken to estimate the mean weight of all adult males.
Correct Answers:
• C
• A
• B
Is this study
• A. REPRESENTATIVE?
• B. NON-REPRESENTATIVE?
A simple random sample of voters is taken in order to determine the chances of a certain candidate winning an election.
6. (1 pt) Industry Research polled teenagers on sunscreen
use. The survey revealed that 46% of teenage girls and 30%
of teenage boys regularly use sunscreen before going out in the
sun.
Is this study
• A. REPRESENTATIVE?
• B. NON-REPRESENTATIVE?
Using a sample of 40 patients from a local hospital, researchers measured cholesterol level in an attempt to estimate
the mean cholesterol level of U.S. citizens.
identify the two populations
• A. all teenagers
• B. teenage girls and teenage boys who use sunscreen
regularly
• C. teenage girls and teenage boys
• D. None of the above
Is this study
• A. REPRESENTATIVE?
• B. NON-REPRESENTATIVE?
Correct Answers:
• B
identify the specified attribute
1
•
•
•
•
Grade on Statistics Exam Relative Frequency
Below 50
50 − 59
60 − 69
70 − 79
80 − 89
90 − 100
A. uses sunscreen before going out in the sun
B. being a teenager
C. being a teenage girl or a teenage boy
D. None of the above
are the proportions 0.46 (46%) and 0.30 (30%) population
proportions or a sample proportions?
Correct Answers:
•
•
•
•
•
•
• A. population proportions
• B. sample proportions
• C. None of the above
9. (1 pt)
Correct Answers:
• C
• A
• B
The following data contains days when road rage occured according to a study. The goal of the study is to determine when
road rage occurs most often.
Before leaving a particular restaurant, patrons are asked to
respond to a questionaire containing the questions given below.
For each question, indicate (using the pull-down menu) whether
the possible responses are Interval, Nominal, or Ordinal.
F, Tu, Th, Th, M, M, F, F, F, M, Su, Sa, F, Su, Tu, F, Sa,
M, F, F, Th, F, F, Th, Su, Th, Th, F, F, Sa, M, W, W, Th, Tu, Tu,
W, M, F, F, W, Su, F, Tu, Sa, W, Th
Find the mode of the above data.
? 1. Would your overall rating of this restaurant be excellent, good, fair, or poor?
? 2. Which of the following attributes of this restaurant do
you find most attractive: service, prices, quality of food,
menu options?
? 3. Do you consider our prices to be high, average, or low?
? 4. Have you eaten at this restaurant previously?
Mode =
Correct Answers:
• F
Correct Answers:
•
•
•
•
0.0980392156862745
0.0392156862745098
0.254901960784314
0.274509803921569
0.196078431372549
0.137254901960784
10. (1 pt) For the given data, find Σx, n, and x:
O
N
O
N
x1 = 15, x2 = 12, x3 = 12, x4 = 17, x5 = 13, x6 = 12, x7 = 6, x8 = 11
8. (1 pt)
Grade on Statistics Exam Frequency
Below 50
5
50 − 59
2
60 − 69
13
70 − 79
14
80 − 89
10
90 − 100
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Σx =
n=
x=
Correct Answers:
• 98
• 8
• 12.25
Given the frequency table above, construct the following:
(a) The relative frequency table that corresponds with the
above table.
2
11. (1 pt) The standard deviation is preferable to the range
as a measure of variation because it takes into account all the
observations, not only the largest and the smallest ones
• A. True
• B. False
Now use the same data set, but this time regard it as a population. Calculate the mean and the standard deviation.
population mean =
population standard deviation =
Correct Answers:
•
•
•
•
One major drawback to the standard deviation as a measure of
variation is that it is
• A. Not resistant
• B. Decreasing
• C. Increasing
• D. None of the above
26.3333333333333
7.82623792124926
26.3333333333333
7.37864787372622
14. (1 pt) The timeplot below gives the share price in dollars
of General Electric stock, with the bar chart giving the volume
in millions of shares. The plots are for the one-year period September 2001-September 2002. (Click on the image for a larger
view. )
Correct Answers:
• A
• A
12. (1 pt)
(a) Which of the following is a true statement?
Calculate the mode, mean, and median of the following data:
• A. The price of General Electric stock has been stable
for this year.
• B. There has been a general upward trend in the stock
price over this time period.
• C. The price should return to 40 dollars within six
months because of the cycle.
• D. There has been a general downward trend in the
stock price over this time period.
• E. None of the above.
(b) If you bought a single share of stock at the maximum
price and sold it at the minimum price during this one-year period, you would have lost about
13, 16, 11, 18, 8, 13, 12, 13
Mode =
Mean =
Median =
Correct Answers:
• 13
• 13
• 13
• A. 45 dollars.
• B. 25 dollars.
• C. 35 dollars.
• D. 15 dollars.
• E. Cannot be determined from the graph.
(c) The maximum price per share for this time period was
about
13. (1 pt)
The length (in pages) of math research projects is given below. Using this information, calculate the mean and the standard
deviation regarding the data set as a sample.
•
•
•
•
•
24, 22, 23, 22, 31, 14, 26, 35, 40
sample mean =
sample standard deviation =
A. 41 dollars.
B. 20 dollars.
C. 45 dollars.
D. 25 dollars.
E. None of the above.
Correct Answers:
• D
• D
3
• A
Correct Answers:
• D
• B
• D
15. (1 pt) Consider the histogram given below: (Click on the
image for a larger view. )
17. (1 pt) Consumers Union measured the gas mileage in
miles per gallon of 38 1978-79 model automobiles on a special
test track. The pie chart below provides information about the
country of manufacture of the model cars used by Consumers
Union. (Click on the image for a larger view. )
(a) Which of the following is a correct statement?
• A. The histogram is symmetric.
• B. The tallest person must have a height of at least 79
inches.
• C. Approximately half the students have heights between 65 and 71 inches.
• D. None of the above are correct.
(b) The interval that contains closest to 10 students is
•
•
•
•
•
(a) Based on this pie chart, we may conclude that
• A. more than half of the cars in the study were from the
United States.
• B. Mercedes Benz, Audi, Porsche, and BMW represent
approximately one quarter of the cars tested.
• C. Japanese cars get significantly lower gas mileage
than cars of other countries. This is because their slice
of the pie is at the bottom of the chart.
• D. Swedish cars get gas mileages that are between those
of Japanese and American cars.
• E. None of the above.
(b) A pie chart is equivalent to a
A. 74-80 inches.
B. 68-71 inches.
C. 59-65 inches.
D. 56-68 inches.
E. None of the above.
Correct Answers:
• D
• B
16. (1 pt) In a statistics class with 136 students, the professor
records how much money each student has in their possession
during the first class of the semester. The histogram below is of
the data collected. (Click on the image for a larger view. )
•
•
•
•
•
A. timeplot
B. histogram.
C. scatter plot.
D. bar chart.
E. None of the above.
Correct Answers:
• A
• D
(a) The histogram
• A. is asymmetric.
• B. is skewed right.
• C. has an outlier.
• D. all of the above.
(b) The percentage of students with over 20 dollars in their
possession is
18. (1 pt)
Data set A:
• A. over 40%.
• B. about 20%.
• C. about 10%.
• D. about 30%.
(c) The number of students with under 10 dollars in their
possession is closest to
Data set C:
•
•
•
•
81, 83, 84, 86, 87, 90
Data set B:
7, 7, 11, 13, 18, 21
6, 7, 8, 8, 8, 10
Above are three different data sets. Without calculating anything, decide which set A, B, or C has the smaller standard
deviation. Just enter the letter of the data set as your answer.
A. 50
B. 40
C. 70
D. 60
Correct Answers:
• C
4
set:
19. (1 pt) For each of the given the data sets below, calculate
the mean, variance, and standard deviation.
(a) 80, 51, 15, 5, 99, 89, 62, 21, 10
standard deviation =
mean =
(b) 55, 48, 46, 51, 40, 51
mean =
standard deviation =
(c) 4.1, 3.9, 2.3, 3.8, 2.6
mean =
standard deviation =
Correct Answers:
• 14
• 52
• 31.636
• 28
• 30.167
• 33.333
• 27.5
• 29.5
Correct Answers:
•
•
•
•
•
•
48
36.4383040220041
48.5
5.16720427310553
3.34
0.826438140455775
22. (1 pt) Calculate the mean and median of the following
grades on a math test:
89, 82, 76, 73, 73, 72, 69, 69, 54, 40, 24
Mean =
20. (1 pt)
Consider the following data set. Find the mean and standard
deviation.
Data set: 74, 44, 62, 54, 85
Median =
Is this data set skewed to the right, symmetric, or skewed to
the left?
(Enter SR, SYM, or SL);
Mean:
Standard deviation:
Correct Answers:
• 65.5454545454545
• 72
• SL
If the data value 63 was added to the set, would the standard
deviation become larger (L) or smaller (S).
You do not need to calculate this second standard deviation
to answer this question.
23. (1 pt) Calculate the 5 number summary and the interquartile range of the following data:
L or S:
44, 36, 28, 62, 39, 40, 69, 32, 22, 50, 46, 12, 37, 17, 54
Correct Answers:
• 63.8
• 16.1616830806695
• S
Q1 =
21. (1 pt) Consider the data set given below:
Q2 =
27, 31, 23, 52, 47, 41, 37, 14, 28, 23, 25
Q3 =
a)Find the minimum value of the data set:
b)Find the maximum value of the data set:
c)Find the arithmetic mean of the data set:
d)Find the median of the data set:
Min =
Max =
Let’s include one more data point in the data set. Suppose
this new data value lies between the values 14 and 52, inclusively.
e)Find the smallest possible value of the mean of the new data
set:
f)Find the largest possible value of the mean of the new data
set:
g)Find the smallest possible value of the median of the new data
set:
h)Find the largest possible value of the median of the new data
IQR =
There is a potential outlier in this data set
• A. False
5
• B. True
(b) What is the probability that the sum on the two dice comes
out to be 10?
Correct Answers:
• 28
• 39
• 50
• 12
• 69
• 22
• A
(c) What is the probability that the sum on the two dice comes
out to be 7?
(d) What is the probability that the numbers on the two dice
are equal?
24. (1 pt)
Correct Answers:
• 36
• 0.0833333333333333
• 0.166666666666667
• 0.166666666666667
Calculate the 5 number summary and the interquartile range
of the following data:
40, 26, 60, 56, 34, −39, 12, 30, 31, 14, 38, 48, 72, 6, 42, 22
26. (1 pt) One die is rolled. List the outcomes comprising the
following events: (make sure you use the correct notation with
the set braces , put a comma between each outcome, and do not
put a space between them):
(a) event the die comes up 4 or more
answer:
(b) event the die comes up even
answer:
(c) event the die comes up 3
answer:
Q1 =
Q2 =
Q3 =
Min =
Correct Answers:
• {4,5,6}
• {2,4,6}
• {3}
Max =
IQR =
27. (1 pt) (Note that an Ace is considered a face card for
this problem)
In drawing a single card from a regular deck of 52 cards we
have:
(a) P( black or a face card ) =
(b) P( Queen and a 3 ) =
(c) P( black and a Queen ) =
(d) P( face card or a number card ) =
(e) P( black and a face card ) =
There is a potential outlier in this data set
• A. True
• B. False
Correct Answers:
• 34/52
• 0/52
• 2/52
• 52/52
• 8/52
Correct Answers:
• 18
• 32.5
• 45
• -39
• 72
• 27
• A
28. (1 pt) Consider the experiment where a pair of fair dice
is thrown.
Let X denote the random variable whose
value is determined by taking the maximum of the spots showing on
either of the two dice thrown.
For example, if a 3 and a 5 were thrown, then X would
take the value of Maximum(3,5) = 5.
The range of values that X can assume are the
positive integers 1,2,3,4,5,6.
25. (1 pt) Two six-sided dice are rolled (one red and
one green).
Some possibilities are (Red=1,Green=5) or
(Red=2,Green=2) etc.
(a) How many total possibilities are there?
For the rest of the questions, we will assume that the dice are
fair and that all of the possibilities in (a) are equally likely.
6
• B. At least three quarters of the data values represented
in D1 are greater than the median value of D3 .
• C. At least one quarter of the data values for D3 are less
than the median value for D2
• D. The data represented in D2 is symmetric.
• E. The data for D1 has a greater median value than the
data for D3 .
Please give the corresponding probabilities for the values
of X given below.
Pr(X = 1) =
Pr(X = 2) =
Pr(X = 3) =
Pr(X = 4) =
Pr(X = 5) =
Pr(X = 6) =
Further, find the probability that X is divisible by 3.
Probability that X is divisible by 3 equals
Correct Answers:
Correct Answers:
•
•
•
•
•
•
•
• ABCE
0.0277777777777778
0.0833333333333333
0.138888888888889
0.194444444444444
0.25
0.305555555555556
0.444444444444444
31. (1 pt) Harry tosses a nickel 4 times.
The probability that he gets at least as many heads as tails is
.
Solution
Notice that he can get 4 heads in just one way: namely
HHHH.
He can get 3 heads in four ways:
HHHT (that is, a tail on his last toss), HHTH ( a tail on his next
to last toss), HTHH, and THHH ;
He can get 2 heads in 6 ways: HHTT, HTHT, HTTH, THHT,
THTH, THHT, TTHH.
Since there are 24 = 16 ordered ways that the nickel can land,
the probability
of at least two heads (which guarantees that he gets at least as
many heads as tails)
11
is 6+4+1
16 = 16 .
Another way of thinking of it is that after computing the number of ways of getting
4, 3, 2 heads, we know there are 5 ways that heads exceed tail
and that means that there must be 5 ways that tails exceed heads
so we don’t
really need to do anything more to know the denominator.
29. (1 pt)
The boxplot below represents annual salaries of attorneys in
thousands of dollars in Los Angeles. About what percentage of
the attorneys have salaries between $155, 000 and $299, 000?
•
•
•
•
A. 40%
B. 75%
C. 80%
D. None of the Above
Correct Answers:
• 11/16
Correct Answers:
32. (1 pt) A red die (sometimes called a number cube) and a
blue die are tossed
Determine the probability of the red die showing a 3 and the
blue die showing a 4 as a reduced fraction.
Solution
The probability of the red die showing a 3 is 16 since the die
has six
faces and only one shows a 3. Similarly the probability of the
blue die showing a 4 is 61 .
1
So the probability of both happening is 16 × 16 = 36
• B
30. (1 pt)
Correct Answers:
• 1/36
33. (1 pt) If A and B are two mutually exclusive events with
P(A) = 0.3 and P(B) = 0.6, find the following probabilities:
a) P(A and B) =
b) P(A or B) =
c) P(not A) =
Which of the following are true?
• A. All the data values for boxplot D1 are greater than
the median value for D2 .
7
A : { Either 3 or 5 occurs }
d) P(not B) =
e) P(not (A or B)) =
f) P(A and (not B)) =
B : { Either 3, 1, or 4 occurs }
Correct Answers:
• 0
• 0.9
• 0.7
• 0.4
• 0.1
• 0.3
C : { 2 does not occur }
P(A) =
P(B) =
P(C) =
Correct Answers:
• 0.5
• 0.55
• 0.85
34. (1 pt) If P(A) = 0.7, P(B) = 0.45 and P(A and B) = 0.2,
find the following probabilities:
a) P(A or B) =
b) P(not A) =
c) P(not B) =
d) P(A and (not B)) =
e) P(not (A and B)) =
36. (1 pt) A fair coin is tossed three times and the events A,
B, and C are defined as follows:
A : { At least one head is observed }
Correct Answers:
• 0.95
• 0.3
• 0.55
• 0.5
• 0.8
B : { At least two heads are observed }
C : { The number of heads observed is odd }
35. (1 pt)
The sample space for an experiment contains five sample
points. The probabilities of the sample points are:
Find the following probabilities by summing the probabilities of the appropriate sample points:
(a) P(A) =
P(1) = P(2) = 0.15
(b) P(A ∩C) =
P(3) = P(4) = 0.2
(c) P(A ∩ B ∩C) =
Correct Answers:
P(5) = 0.3
Find the probability of each of the following events:
• 0.125
• 0.375
• 0.125
c
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