STAT 200 Introduction to Statistics Final Examination, Sp.docx

STAT 200: Introduction to Statistics Final Examination,
Spring 2016 OL4 Page 1 of 7
STAT 200
OL4/US2 Sections
Final Exam
Spring 2016
The final exam will be posted at 12:01 am on May 6, and it is
due
at 11:59 pm on May 8, 2016. Eastern Time is our reference
time.
This is an open-book exam. You may refer to your text and
other course materials
as you work on the exam, and you may use a calculator. You
must complete the
exam individually. Neither collaboration nor consultation with
others is allowed.
It is a violation of the UMUC Academic Dishonesty and
Plagiarism policy to use

unauthorized materials or work from others.
Answer all 20 questions. Make sure your answers are as
complete as possible.
Show all of your work and reasoning. In particular, when there
are calculations
involved, you must show how you come up with your answers
with critical work
and/or necessary tables. Answers that come straight from
calculators, programs
or software packages will not be accepted. If you need to use
software (for
example, Excel) and /or online or hand-held calculators to aid in
your calculation,
you must cite the sources and explain how you get the results.
Record your answers and work on the separate answer sheet
provided.
This exam has 200 total points; 10 points for each question.
You must include the Honor Pledge on the title page of your
submitted final exam.
Exams submitted without the Honor Pledge will not be

accepted.
1. True or False. Justify for full credit.
(a) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then
P(A AND B) = 0.2.
(b) If all the observations in a data set are identical, then the
variance for this data set is 0.
(c) The mean is always equal to the median for a normal
distribution.
(d) It’s easier to reject the null hypothesis at significance level
of 0.01 than at significance
level of 0.05.
(e) In a two-tailed test, the value of the test statistic is 2. If we
know the test statistic follows a
Student’s t-distribution with P(T >2) = 0.03, then we have
sufficient evidence to reject the
null hypothesis at 0.05 level of significance.

2. Identify which of these types of sampling is used: cluster,
convenience, simple random,
systematic, or stratified. Justify for full credit.
(a) The quality control department of a semiconductor
manufacturing company tests every 100
th
product from the assembly line.
(b) UMUC STAT Club wanted to estimate the study hours of
STAT 200 students. Two STAT 200
sections were randomly selected and all students from these two
sections were asked to fill out
the questionnaire.
(c) A STAT 200 student is interested in the number of credit
cards owned by college students. She
surveyed all of her classmates to collect sample data.
(d) In a career readiness research, 100 students were randomly
selected from the psychology
program, 150 students were randomly selected from the
communications program, and 120
students were randomly selected from cyber security program.

3. The frequency distribution below shows the distribution for
commute time (in minutes) for a
sample of 50 STAT 200 students on a Friday afternoon. (Show
all work. Just the answer,
without supporting work, will receive no credit.)
Commute Time (in minutes) Frequency Relative Frequency
1 – 14.9 5
15 – 29.9 10
30 – 44.9
0.20
45 – 59.9 20
60 or above
Total 50
(a) Complete the frequency table with frequency and relative
frequency. Express the relative

frequency to two decimal places.
(b) What percentage of the commute times was at least 30
minutes?
(c) Does this distribution have positive skew or negative skew?
Why?
4. The five-number summary below shows the grade distribution
of two STAT 200 quizzes for a
sample of 500 students.
Minimum Q1 Median Q3 Maximum
Quiz 1 15 35 55 85 100
Quiz 2 20 35 50 90 100
For each question, give your answer as one of the following: (i)
Quiz 1; (ii) Quiz 2; (iii) Both quizzes
have the same value requested; (iv) It is impossible to tell using
only the given information. Then

explain your answer in each case.
(a) Which quiz has less range in grade distribution?
(b) Which quiz has the greater percentage of students with
grades 85 and over?
(c) Which quiz has a greater percentage of students with grades
less than 60?
5. A box contains 3 marbles, 1 red, 1 green, and 1 blue.
Consider an experiment that consists of
taking 1 marble from the box, then replacing it in the box and
drawing a second marble from
the box. (Show all work. Just the answer, without supporting
work, will receive no credit.)
(a) List all outcomes in the sample space.
(b) What is the probability that neither marble is red? (Express
the answer in simplest
fraction form)
6. There are 1000 students in a high school. Among the 1000
students, 250 students take AP
Statistics, and 300 students take AP French. 100 students take

both AP courses. Let S be the
event that a randomly selected student takes AP Statistics, and F
be the event that a randomly
selected student takes AP French. Show all work. Just the
answer, without supporting work,
will receive no credit.
(a) Provide a written description of the complement event of (S
OR F).
(b) What is the probability of complement event of (S OR F)?
7. Consider rolling two fair dice. Let A be the event that the
sum of the two dice is 8, and B be
the event that the first one lands on 6.
(a) What is the probability that the first one lands on 6 given
that the sum of the two dice is 8?
Show all work. Just the answer, without supporting work, will
receive no credit.
(b) Are event A and event B independent? Explain.

8. There are 8 books in the “Statistics is Fun” series. (Show all
work. Just the answer, without
supporting work, will receive no credit).
(a) How many different ways can Mimi arrange the 8 books in
her book shelf?
(b) Mimi plans on bringing two of the eight books with her in a
road trip. How many different
ways can the two books be selected?
9. Assume random variable x follows a probability distribution
shown in the table below.
Determine the mean and standard deviation of x. Show all work.
Just the answer, without
supporting work, will receive no credit.
x -2 0 1 3 5
P(x) 0.1 0.2 0.3 0.1 0.3
10. Mimi plans on growing tomatoes in her garden. She has 15

cherry tomato seeds. Based on her
experience, the probability of a seed turning into a seedling is
0.40.
(a) Let X be the number of seedlings that Mimi gets. As we
know, the distribution of X is a
binomial probability distribution. What is the number of trials
(n), probability of successes (p)
and probability of failures (q), respectively?
(b) Find the probability that she gets at least 2 cherry tomato
seedlings. (round the answer to 3
decimal places) Show all work. Just the answer, without
11. Assume the weights of men are normally distributed with a
mean of 172 lbs and a standard
deviation of 30 lbs. Show all work. Just the answer, without
supporting work, will receive no
credit.
(a) Find the 90
th
percentile for the distribution of men’s weights.

(b) What is the probability that a randomly selected man weighs
more than 185 lbs?
12. Assume the IQ scores of adults are normally distributed
with a mean of 100 and a standard
deviation of 15. Show all work. Just the answer, without
(a) If a random sample of 25 adults is selected, what is the
standard deviation of the sample mean?
(b) What is the probability that 25 randomly selected adults will
have a mean IQ score that is
between 95 and 105?
13. A survey showed that 80% of the 1600 adult respondents
believe in global warming. Construct a
95% confidence interval estimate of the proportion of adults
believing in global warming. Show
all work. Just the answer, without supporting work, will receive
no credit.

14. In a study designed to test the effectiveness of acupuncture
for treating migraine, 100 patients
were randomly selected and treated with acupuncture. After
one-month treatment, the number of
migraine attacks for the group had a mean of 2 and standard
deviation of 1.5. Construct a 95%
confidence interval estimate of the mean number of migraine
attacks for people treated with
acupuncture. Show all work. Just the answer, without
15. Mimi is interested in testing the claim that more than 75%
of the adults believe in global
warming. She conducted a survey on a random sample of 100
adults. The survey showed that
80 adults in the sample believe in global warming.
Assume Mimi wants to use a 0.05 significance level to test the
claim.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the

correct test statistic, without supporting
work, will receive no credit.
(c) Determine the P-value for this test. Show all work; writing
the correct P-value, without
(d) Is there sufficient evidence to support the claim that more
than 75% of the adults believe in
global warming? Explain.
16. In a study of memory recall, 5 people were given 10 minutes
to memorize a list of 20 words.
Each was asked to list as many of the words as he or she could
remember both 1 hour and 24
hours later. The result is shown in the following table.
Number of Words Recalled
Subject 1 hour later 24 hours later
1 14 12
2 18 15
3 11 9
4 13 12

5 12 12
Is there evidence to suggest that the mean number of words
recalled after 1 hour exceeds the
mean recall after 24 hours?
Assume we want to use a 0.10 significance level to test the
claim.
(d) Is there sufficient evidence to support the claim that the
mean number of words recalled after 1
hour exceeds the mean recall after 24 hours? Justify your
conclusion.

17. In a pulse rate research, a simple random sample of 40 men
results in a mean of 80 beats per
minute, and a standard deviation of 11.3 beats per minute.
Based on the sample results, the
researcher concludes that the pulse rates of men have a standard
deviation greater than 10 beats
per minutes. Use a 0.05 significance level to test the
researcher’s claim..
(a) Identify the null hypothesis and alternative hypothesis.
correct test statistic, without
(d) Is there sufficient evidence to support the researcher’s
claim? Explain.
18. The UMUC MiniMart sells four different types of teddy
bears. The manager reports that the
four types are equally popular. Suppose that a sample of 500

purchases yields observed counts
150, 120, 110, and 120 for types 1, 2, 3, and 4, respectively.
Type 1 2 3 4
Number 150 120 110 120
Assume we want to use a 0.05 significance level to test the
claim that the four types are
equally popular.
correct test statistic, without
(c) Determine the critical value. Show all work; writing the
correct critical value, without
(d) Is there sufficient evidence to support the manager’s claim
that the four types are equally
popular? Justify your answer.
19. A random sample of 4 professional athletes produced the
following data where x is the number

of endorsements the player has and y is the amount of money
made (in millions of dollars).
x 0 1 2 5
y 1 2 4 8
(a) Find an equation of the least squares regression line. Show
all work; writing the correct
equation, without supporting work, will receive no credit.
(b) Based on the equation from part (a), what is the predicted
value of y if x = 3? Show all work
and justify your answer.
20. A study of 10 different weight loss programs involved 500
subjects. Each of the 10 programs had
50 subjects in it. The subjects were followed for 12 months.
Weight change for each subject was
recorded. Mimi wants to test the claim that the mean weight

loss is the same for the 10 programs.
(a) Complete the following ANOVA table with sum of squares,
degrees of freedom, and mean
square (Show all work):
Source of
Variation
Sum of Squares
(SS)
Degrees of
Freedom (df)
Mean Square
(MS)
Factor
(Between)
42.36
Error
(Within)

Total 1100.76
N/A
(d) Is there sufficient evidence to support the claim that the
mean weight loss is the same for the
10 programs at the significance level of 0.05? Explain.
STAT 200 Final ExaminationSpring 2016 OL4/US2Page 1 of 9
STAT 200 Introduction to Statistics
Name______________________________
Final Examination: Spring 2016 OL4/US2 Instructor
__________________________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and
other course materials as you work on the exam, and you may
use a calculator.
Record your answers and work in this document.
Answer all 20 questions. Make sure your answers are as
complete as possible. Show all of your work and reasoning. In

particular, when there are calculations involved, you must show
how you come up with your answers with critical work and/or
necessary tables. Answers that come straight from calculators,
programs or software packages will not be accepted. If you need
to use software (for example, Excel) and /or online or hand-held
calculators to aid in your calculation, please cite the source and
explain how you get the results.
When requested, show all work and write all answers in the
spaces allotted on the following pages. You may type your
work using plain-text formatting or an equation editor, or you
may hand-write your work and scan it. In either case, show
work neatly and correctly, following standard mathematical
conventions. Each step should follow clearly and completely
from the previous step. If necessary, you may attach extra
pages.
You must complete the exam individually. Neither
collaboration nor consultation with others is allowed. It is a
violation of the UMUC Academic Dishonesty and Plagiarism
policy to use unauthorized materials or work from others. Your
exam will receive a zero grade unless you complete the
following honor statement.
Please sign (or type) your name below the following honor
statement:
I understand that it is a violation of the UMUC Academic
Dishonesty and Plagiarism policy to use unauthorized materials
or work from others. I promise that I did not discuss any aspect
of this exam with anyone other than my instructor. I further
promise that I neither gave nor received any unauthorized
assistance on this exam, and that the work presented herein is
entirely my own.
Name _____________________Date___________________
Record your answers and work.

Problem Number
Solution
1
Answer:
(a)
(b)
(c)
(d)
(e)
Justification:

2
Answer:
(a)
(b)
(c)
(d)
Justification:

3
Answer:
(a)
Commute Time (in minutes)
Frequency
Relative Frequency
1 – 14.9
5
15 – 29.9
10
30 – 44.9
0.20
45 – 59.9
20
60 or above
Total

50
(b)
(c)
Work for (a) and (b):
4
Answer:
(a)
(b)

(c)
Justification :
5
Answer:
(a)
(b)
Work for (b):
6

Answer:
(a)
(b)
Work for (b):
7
Answer:
(a)
(b)
8

Answer:
(a)
(b)
9
Answer:
Work:

10
Answer:
(a)
(b)
Work for (b) :
11
Answer:
(a)
(b)

12
Answer:
(a)
(b)

13
Answer:
Work:
14
Answer:
Work:
15
Answer:
(a)

(b)
(c)
(d)
Work for (b) and (c):
16
Answer:
(a)
.
(b)
(c)

(d)
17
Answers:
(a)
(b)
(c)
(d).

18
Answer:
(a)
(b)
(c)
(d)

19
Answer:
(a)
(b)

20
Answer :
(a)
Source of Variation
Sum of Squares
(SS)
Degrees of Freedom (df)
Mean Square (MS)
Factor
(Between)
42.36
Error
(Within)

Total
1100.76
N/A
(b)
(c)
(d)
Work for (a), (b) and (c)

STAT 200 Introduction to Statistics Final Examination, Sp.docx

STAT 200 Introduction to Statistics Final Examination, Sp.docx

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STAT 200 Introduction to Statistics Final Examination, Sp.docx