STAT 200 Introduction to Statistics Final Examination, Spri.docx

STAT 200: Introduction to Statistics
Final Examination, Spring 2019 OL3
Page 1 of 8
STAT 200
OL3 Sections
Final Exam
Spring 2019
The final exam will be posted at 12:01 am on April 19, 2019,
and
it is due at 11:59 pm on April 21, 2019 Eastern Time.
This is an open-book exam. You may refer to your text and
other course materials
for the current course as you work on the exam, and you may
use a calculator,
applets, or Excel. 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,
particularly when it asks for you to show your work. Answers
that come straight
from calculators, programs or software packages without any
explanation will not
be accepted. If you need to use technology (for example, Excel,
online or hand-
held calculators, statistical packages) to aid in your calculation,
you must cite the
sources and explain how you get the results. For example, state
the Excel function
along with the required parameters when using Excel; describe
the detailed steps
when using a hand-held calculator; or provide the URL and
detailed steps when
using an online calculator, and so on.

Record your answers and work on the separate answer sheet
provided.
This exam has 20 problems; 5% for each problems.
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.
Page 2 of 8
1. You wish to estimate the mean cholesterol levels of patients
two days after they had a heart attack. To
estimate the mean, you collect data from 28 heart patients.
Justify for full credit.
(a) Which of the followings is the sample?
(i) Mean cholesterol levels of 28 patients recovering from a

heart attack suffered two
days ago
(ii) Cholesterol level of the person recovering from heart attack
suffered two days ago
(iii) Set of all patients recovering from a heart attack suffered
two days ago
(iv) Set of 28 patients recovering from a heart attack suffered
two days ago
(b) Which of the followings is the variable?
(i) Mean cholesterol levels of 28 patients recovering from a
heart attack suffered two
days ago
(ii) Cholesterol level of the person recovering from heart attack
suffered two days ago
(iii) Set of all patients recovering from a heart attack suffered
two days ago
(iv) Set of 28 patients recovering from a heart attack suffered
two days ago
2. In order to collect data on the number of courses that your
classmates take in this semester, you plan
on asking them: “How many UMUC courses are you taking in

this semester? “Justify for full credit.
(a) Which type of data will you collect?
(i) Discrete
(ii) Continuous
(iii) Qualitative
(iv) Cannot be determined
(b) Which measure of variation can be used to summarize your
data?
(i) Mean
(ii) Median
(iii) Mode
(iv) Variance
Page 3 of 8

3. True or False. Justify for full credit.
(a) If the variance from a data set is zero, then all the
observations in this data set
must be identical.
(b) The median of a normal distribution curve is always zero.
4. 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.
(a) What type of sampling method is being used?
(b) Please explain your answer.
5. A study was conducted to determine whether the mean
braking distance of four-cylinder cars is
greater than the mean braking distance of six-cylinder cars. A
random sample of 20 four-cylinder cars
and a random sample of 20 six-cylinder cars were obtained, and
the braking distances were measured.

(a) What would be the appropriate hypothesis test for this
analysis?
(i) t-test for two dependent samples
(ii) t-test for two independent samples
(iii) z-test for two population means
(iv) correlation
(b) Explain the rationale for your selection in (a). Specifically,
why would this be the appropriate
statistical approach?
6. 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. The researcher wants to test the claim that all ten
programs are equally effective in weight
loss.
(a) Which statistical approach should be used?
(i) confidence interval
(ii) t-test
(iii) ANOVA

(iv) Chi square
(b) Explain the rationale for your selection in (a). Specifically,
why would this be the appropriate
statistical approach?
Page 4 of 8
7. A random sample of 80 customers was chosen in UMUC
MiniMart between 3:00 and 4:00 PM on a
Friday afternoon. The frequency distribution below shows the
distribution for checkout time (in
minutes). (Show all work. Just the answer, without supporting
work, will receive no credit.)
Checkout Time (in
Minutes) Frequency
Cumulative Relative
Frequency

1.0 – 1.9 0.10
2.0 – 2.9 0.65
3.0 – 3.9 16
4.0 – 4.9 8
5.0 – 5.9 4 1.00
Total 80
(a) Complete the frequency table with frequency and cumulative
relative frequency. Express
the cumulative relative frequency to two decimal places.
(b) What percentage of the checkout times was less than 4
minutes?
(c) Which of the following checkout time groups does the
median of this distribution belong
to? 1.0 – 1.9, 2.0 – 2.9, 3.0 – 3.9, 4.0 – 4.9, or 5.0 – 5.9? Why?
8. There are 15 members on the board of directors for a Fortune
500 company. If they must select a
chairperson, a first vice chairperson, a second vice chairperson,
and a secretary.
(a) How many different ways the officers can be selected?
(b) Please describe the method used and the reason why it is
appropriate for answering the question.

Just the answer, without the description and reason, will receive
no credit.
9. A researcher wants to conduct a clinical trial on a new
medicine for a rare disease. She plans
to randomly choose 4 testers from 20 eligible patients.
(a) How many different ways can the testers be chosen?
(b) Please describe the method used and the reason why it is
appropriate for answering the
question. Just the answer, without the description and reason,
will receive no credit.
10. Consider selecting one ball at a time from a box which
contains 10 red, 6 yellow and 4 blue balls.
What is the probability that the first ball is yellow and the
second ball is also yellow? Express the
probability in fraction format. (Show all work. Just the answer,
without supporting work, will receive
no credit.)
(a) Assuming the ball selection is without replacement.
(b) Assuming the ball selection is with replacement.

Page 5 of 8
11. An airline company has a policy of routinely overbooking
flights. The following probability
distribution table shows the random variable, x, where x is
number of passengers who cannot be
boarded because there are more passengers than seats:
x P(x)
0 0.07
1 0.14
2 0.27
3 0.33
4 0.19
(a) Determine the mean of x (Round the answer to two decimal
places). Show all work. Answers

without supporting work will not receive credit.
(b) Determine the standard deviation of x. (Round the answer to
two decimal places) Show all
work. Answers without supporting work will not receive credit.
12. 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
0.60.
(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 10 cherry tomato
seedlings. (Round the answer to 3
decimal places) Show all work. Just the answer, without
supporting work, will receive no
credit.
Refer to the following information for Questions 13 and 14.
The heights of pecan trees are normally distributed with a mean
of 10 feet and a

standard deviation of 2 feet.
13. Show all work. Just the answer, without supporting work,
(a) What is the probability that a randomly selected pecan tree
is between 9 and 12 feet tall?
(Round the answer to 4 decimal places)
(b) Find the 80th percentile of the pecan tree height
distribution. (Round the answer to 2 decimal
places)
14. Show all work. Just the answer, without supporting work,
(a) For a sample of 36 pecan trees, state the standard deviation
of the sample mean (the "standard
error of the mean"). (Round your answer to three decimal
places)
(b) Suppose a sample of 36 pecan trees is taken. Find the
probability that the sample mean
heights is between 9.5 and 10 feet. (Round your answer to four
decimal places)

Page 6 of 8
15. A survey showed that 750 of the 1000 adult respondents
believe in global warming.
(a) Construct a 95% confidence interval estimate of the
proportion of adults believing in global
warming. (Round the lower bound and upper bound of the
confidence interval to three decimal
places) Include description of how confidence interval was
constructed.
(b) Describe the results of the survey in everyday language.
16. A bike company wants to determine how long children have
to use training wheels when learning to
ride two-wheel bikes. The company surveyed a random sample
of 64 children. The result showed that
they used an average of 180 days with a sample standard
deviation of 100 days.
(a) Construct a 95% confidence interval estimate of the mean
length of time using training wheels.

(Round the lower bound and upper bound of the confidence
interval to whole number) Include
description of how confidence interval was constructed.
(b) Describe the confidence interval in everyday language.
17. An AP Statistics teacher claims that the AP Statistics grade
distribution is as follows:
Grade A B C D F
Percentage 20% 40% 20% 15% 5%
Suppose that a sample of 100 students taking AP Statistics class
yields the observed counts shown
below:
Grade A B C D F
Number of
Students
25 35 15 17 8
Use a 0.10 significance level to test the claimed AP Statistics
grade distribution is correct.

(a) Identify the appropriate hypothesis test and explain the
reasons why it is appropriate for analyzing
this data.
(b) Identify the null hypothesis and the alternative hypothesis.
(c) Determine the test statistic. (Round your answer to two
decimal places)
(d) Determine the p-value. (Round your answer to two decimal
places)
(e) Compare p-value and significance level α. What decision
should be made regarding the null
hypothesis (e.g., reject or fail to reject) and why?
(f) Is there sufficient evidence to support that the claimed AP
Statistics grade distribution is correct?
Justify your answer.
Page 7 of 8
18. 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.
Does the data below suggest that the mean number of words

recalled after 1 hour exceeds the mean
recall after 24 hours? Assume we want to use a 0.05
significance level to test the claim.
Number of Words Recalled
Subject 1 hour later 24 hours later
1 14 12
2 18 14
3 11 8
4 13 12
5 12 12
(a) What is the appropriate hypothesis test to use for this
analysis? Please identify and explain why
it is appropriate.
(b) Let μ1 = mean words recalled after 1 hour. Let μ2 = mean
words recalled after 24 hours. Which
of the following statements correctly defines the null
hypothesis?
(i) μ1 - μ2 > 0 (μd > 0)
(ii) μ1 - μ2 = 0 (μd = 0)
(iii) μ1 - μ2 < 0 (μd < 0)

(c) Let μ1 = mean words recalled after 1 hour. Let μ2 = mean
words recalled after 24 hours. Which
of the following statements correctly defines the alternative
hypothesis?
(i) μ1 - μ2 > 0 (μd > 0)
(ii) μ1 - μ2 = 0 (μd = 0)
(iii) μ1 - μ2 < 0 (μd < 0)
(d) Determine the test statistic. Round your answer to three
decimal places. Describe method used
for obtaining the test statistic.
(e) Determine the p-value. Round your answer to three decimal
places. Describe method used for
obtaining the p-value.
(f) Compare p-value and significance level α. What decision
(g) What do the results of this study tell us about the mean
number of words recalled after 1 hours and
after 24 hours? Justify your conclusion.

of 8
19. A grocery store manager is interested in testing the claim
that banana is the favorite fruit for more
than 50% of the adults. The manager conducted a survey on a
random sample of 100 adults. The
survey showed that 56 adults in the sample chose banana as
his/her favorite fruit. Assume the
manager wants to use a 0.05 significance level to test the claim.
(a) What is the appropriate hypothesis test to use for this
analysis? Please identify and explain
why it is appropriate.
(b) Identify the null hypothesis and the alternative hypothesis.
(c) Determine the test statistic. Round your answer to two
decimal places. Describe method used
for obtaining the test statistic
(d) Determine the p-value. Round your answer to three decimal
places. Describe method used for
obtaining the p-value
(e) Compare p-value and significance level α. What decision
(f) Is there sufficient evidence to support the claim that banana
is the favorite fruit for more than
50% of the adults? Explain your conclusion.

20. A random sample of 8 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 y
0 1
1 1.5
1 2
2 3
2 3.5
3 3
5 6.5
5 7
(a) Find an equation of the least squares regression line. Round
the slope and y-intercept
value to two decimal places. Describe method for obtaining
results.
(b) Based on the equation from part (a), what is the predicted
amount of money made when a
professional athlete has 4 endorsements? Show all work and
justify your answer.

(c) Based on the equation from part (a), what is the predicted
amount of money made when a
professional athlete has 15 endorsements? Show all work and
justify your answer.
(d) Which predicted amount of money made that you calculated
for (b) and (c) do you think is closer
to the true amount of the money made and why?
STAT 200 Final ExaminationSpring 2019 OL3Page 2 of 5
STAT 200 Introduction to Statistics
Name______________________________
Final Examination: Spring 2019 OL3 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 without explanation will not be
accepted. If you need to use technology to aid in your
calculation, you have to cite the source and explain how you get
the results. For example, state the Excel function along with the
required parameters when using Excel; describe the detailed
steps when using a hand-held calculator; or provide the URL
and detailed steps when using an online calculator, and so on.

Show all supporting 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)
Justification for (a) and (b):
2
Answer:
(a)
(b)

3
Answer:
(a)
(b)
4
Answer:
(a)
(b)
5

Answer:
(a)
(b)
6
Answer:
(a)
(b)
7
Answer:
(a)

Checkout Time (in Minutes)
Frequency
Cumulative Relative Frequency
1.0 – 1.9
0.10
2.0 – 2.9
0.65
3.0 – 3.9
16
4.0 – 4.9
8
5.0 – 5.9
4
1.00
Total
80
(b)

(c)
Work for (a) and (b):
8
Answer:
(a)
(b)
Work for (a):

9
Answer:
(a)
(b)
Work for (a):
10
Answer:
(a)
(b)

11
Answer:
(a)
(b)

12
Answer:
(a) n = , p = , and q = .
(b)
Work for (b):
13
Answer:
(a)

(b)
14
Answer:
(a)
(b)

15
Answer:
(a)
(b)
Work for (a):

16
Answer:
(a)
(b)
Work for (a):
17
Answer:

(a)
(b)
(c)
(d)
(e)
(f)
Work for (c) and (d):

(d)
(e)
(f)
(g)
Work for (d) and (e):

19
Answer:
(a)
(b)
(c)
(d)
(e)
(f)

Work for (c) and (d):
20
Answer:
(a)
(b)
(c)
(d)

STAT 200 Introduction to Statistics Final Examination, Spri.docx

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