Download Classify the study as either descriptive or inferential

STP 226 Statistics
Diane Richardson
Print name here_________________________
Test #2 Summer 2015
Honor Statement:
By signing below you confirm that you have neither given nor received any unauthorized
assistance on this exam. This includes any use of a graphing calculator beyond those uses
specifically authorized by the Mathematics Department and your instructor. Furthermore,
you agree not to discuss this exam with anyone until the exam testing period is over. In
addition, your calculator’s memory and menus may be checked at any time and cleared by
any testing center proctor or Mathematics Department instructor.
_
Signature
Instructions:
________________________
Date
 The exam is worth a total of 105 points; please make sure your exam has all
pages before you begin. Make sure that you have all 10 pages to your exam.
If you do not have 10 pages, then contact your Instructor.
 Part 1 is Free Response Show all work in detail or your answer will not
receive any credit. Include appropriate units on all questions that apply.
Write neatly and box all answers.
 Part 2 is Multiple Choice Problems 7-16 are worth 6 points and problems
17-19 are worth 4 points. Showing all work in detail will assist you in
obtaining the correct answers and will be reviewed at the Instructor’s
discretion.
 Please ask your instructor if you need scratch paper.
 No calculators or computers that do symbolic algebra, like the Casio
FX-2, TI-89, or TI- 92, may be used.
 A table is given on page seven for you to write in the letter for the
correct answer. You may take these pages off to help you write the
correct letter in for each answer.
 The formulas are on page eight of the exam.
 The z-tables are on the last two pages of the exam.
STP 226 Test 2 - Summer 2015
Page 2
Part 1 is Free Response. Make sure to show all of your work. No work, no credit.
The following table displays the finishing times, in seconds, for the winners of fifteen 1 –
mile thoroughbred horse races, as found in two recent issues of Thoroughbred Times [ 16
points]
94.15
93.37
82.01
95.57
97.73
101.09
99.38
97.19
96.63
101.05
83.05
97.91
98.44
97.47
95.10
If the Normal Scores in ascending order are as follows:
-1.71
-1.23
-0.94
-0.33
-0.16
0
0.52
0.71
0.94
Finishing
times in
sec
-0.71
0.16
1.23
Normal
Score.
A table is provided for your convenience to organize the information.
2. Construct a Normal probability plot of the data
3. Is the data normally distributed? If so why? If not, then why not?
SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences
-0.52
0.33
1.71
STP 226 Test 2 - Summer 2015
Page 3
Use the following information for problems 4-6 to find the requested information (18 pts)
Heights in inches for the population of Five Senior/Junior players on the ASU Water Polo Team
in 2013 included
Player
Weight
Morrison (M)
67
Brightwell (B)
69
Haas (H)
70.5
Young (Y)
70
Silverberg (S)
68
With a population mean µ=68.9 inches.
For a sampling distribution of size n=2 from the population of the five senior players gives mean
heights in the following table
Players
Mean Height
M,B
68
M,H
M,Y
68.5
M,S
67.5
B,H
69.75
Players
Mean Height
B,Y
69.5
B,S
68.5
H,Y
70.25
H,S
69.25
Y,S
69
4. What is the mean height for Morrison and Haas?
5. From the sampling distribution, what is the probability that the mean height of the two players
is within 1 inch of the true mean?
6. If samples of size 4 are to be chosen from the population of size 5 instead of samples of size 2,
how many groups would there be?
SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences
STP 226 Test 2 - Summer 2015
Page 4
Part 2 Multiple Choice
The hours of sleep Americans get on a typical night is shown in the table. For problems 710 use the following table to find the frequencies requested for each of the following events.
Hours of Sleep
4 or less
5
6
7
8
9
10 or more
Sum of Frequencies=
Frequency: Number Americans in millions
12
27
75
90
81
9
6
300
A: at least 7 hours were slept.
C: at most 5 hours were slept.
B: exactly 6 hours were slept.
D: at most 8 hours were slept.
7. Event A
A) 15
B) 285
C) 114
D) 186
E) None of the Above
8. Events (D or C)
A) 15
B) 285
C) 246
D) 324
E) None of the Above
B) 186
C) 15
D) 285
E) None of the Above
B) 0
C) 114
D) 100
E) None of the Above
9. Event ( not D)
A) 114
10. Event ( B and C)
A) 153
SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences
STP 226 Test 2 - Summer 2015
Page 5
A recent study on college students found that 15% smoke, 7.9% have been diagnosed as
having depression, and 5.27% are depressed smokers. For a college student selected at
random, let S be the event that the person is a smoker, and D be the event that the person
has been diagnosed as been depressed. For problems 11 and 12, find the following
probabilities:
11. The probability that the student is a smoker or has been diagnosed with depression.
A) 0.242
B) 0.229
C) 0.71
D) 0.1763
E) None of the Above
12. Find the probability that the person was a non-smoker.
A) 0.921
B) 0.85
C) 0.9473
D) 0.771
E) None of the Above
In questions 13 - 14 use the tables of the standard normal curve to give the 4 decimal place
answer for the area or the 2 decimal place answer for the z-scores.
13. Find the area between 1.25 and 2.13 under N(0,1)
A) 0.8944
B) 0.089
C) 0.1056
D) 0.911
E) None of the Above
14. Find the 40th percentile of the standard normal curve.
A) 0.60
B) 0.25
C) -0.25
D) -0.60
E) None of the Above
SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences
STP 226 Test 2 - Summer 2015
Page 6
Weights of a Beagle dog .
Use the following information for answering the questions below:
The data for this example is for the full grown dog breed known as the Beagle (think
Snoopy). The weight of this breed is normally distributed with a mean of 22.5 pounds and a
standard deviation of 2.2 pounds. Use this information to answer questions
15. Compute the probability that a dog will weigh less than 21.2 pounds
A 0.59
B 0.7224
C 0.2776
D 0.41
E None of the Above
16. If four Beagle dogs are randomly selected what is the probability that the sample mean
X of the four, Beagle dogs more than 24.5 pounds?
A. 0.6372
B. 0.9656
C. 0.8186
D. 0.0344
E. None of these
Short Answer.
17. Normal probability plots are used to determine if a data set has outliers.
A) True
B) False
18. We can use symbolic notation z 0.20 for 80th percentile of N(0,1) distribution
A) True
B) False
19. Suppose the median home value (house or condo) in Tempe, Arizona is $203,000 in 2013 is
right skewed. For the samples of size 64, sample mean x has an approximately normal
distribution.
A. True
B. False
SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences
STP 226 Test 2 - Summer 2015
Page 7
Circle your answer choice on the exam AND fill in the answer with the letter of the answer
that you believe is the correct answer.
Problem
Number
Letter of Answer
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
XXXXXXXXX
XXXXXXXXXX
17.
18.
19
SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences
STP 226 Test 2 - Summer 2015
Page 8
Formulas Exam 2
Probability Rules
f
P( E ) 
n
P(not E )  1  P( E )
P( A or B )  P( A)  P( B)  P( A and B )
n!
n Cr 
n - r !  r !
x
Descriptive Measures:
z
x
n
x-

x
N

Sampling Distribution of X :  x   ,  x 
Standardized version of X :
z

n
,
x
  


 n
SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences
STP 226 Test 2 - Summer 2015
SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences
Page 9
STP 226 Test 2 - Summer 2015
SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences
Page 10