STAT 200: Introduction to Statistics Final Examination, Spring 2016 OL1/US1

STAT 200: Introduction to Statistics

Final Examination, Spring 2016 OL1/US1

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STAT 200
OL1/US1 Sections
Final Exam
Spring 2016
The final exam will be posted at 12:01 am on March 4, and it is
due at 11:59 pm on March 6, 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.

STAT 200: Introduction to Statistics

1.

Final Examination, Spring 2016 OL1/US1

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True or False. Justify for full credit.
(a)
(b)
(c)
(d)
(e)

The standard deviation of a data set cannot be negative.
If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.2.
The mean is always equal to the median for a normal distribution.
A 95% confidence interval is wider than a 98% confidence interval of the same parameter.
In a two-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows
a Student’s t-distribution with P(T < 1.5) = 0.98, then we fail 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)

A STAT 200 professor wants to estimate the study hours of his students. He teaches two
sections, and plans on randomly selecting 10 students from the first section and 15 students
from the second section.
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.
The quality control department of a semiconductor manufacturing company tests every 100th
product from the assembly line.
On the day of the last presidential election, UMUC News Club organized an exit poll in which
specific polling stations were randomly selected and all voters were surveyed as they left those
polling stations.

(b)
(c)
(d)

3.

The frequency distribution below shows the distribution for checkout time (in minutes) in
UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. (Show all work. Just the
answer, without supporting work, will receive no credit.)

Checkout Time (in minutes) Frequency Relative Frequency
1.0 - 1.9

3

2.0 - 2.9

12
0.20

3.0 - 3.9
4.0 - 4.9

3

5.0 -5.9
Total

(a)
(b)
(c)

25

Complete the frequency table with frequency and relative frequency. Express the relative
frequency to two decimal places.
What percentage of the checkout times was at least 4 minutes?
Does this distribution have positive skew or negative skew? Why?

STAT 200: Introduction to Statistics

Final Examination, Spring 2016 OL1/US1

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4.

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)
(b)

List all outcomes in the sample space.
What is the probability that at least one marble is red?
fraction form)

5.

The five-number summary below shows the grade distribution of two STAT 200 quizzes for a
sample of 500 students.

(Express the answer in simplest

Minimum
Quiz 1
Quiz 2

Q1

Median

Q3

Maximum

15
20

30
35

55
50

85
90

100
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)
(b)
(c)

Which quiz has less interquartile range in grade distribution?
Which quiz has the greater percentage of students with grades 90 and over?
Which quiz has a greater percentage of students with grades less than 50?

6.

There are 1000 students in a high school. Among the 1000 students, 800 students have a
laptop, and 300 students have a tablet. 250 students have both devices. Let L be the event that
a randomly selected student has a laptop, and T be the event that a randomly selected student
has a tablet. Show all work. Just the answer, without supporting work, will receive no credit.

(a)
(b)

Provide a written description of the event L OR T.
What is the probability of event L OR T?

7.

Consider rolling two fair dice. Let A be the event that the two dice land on different numbers,
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 two dice land on different
numbers? Show all work. Just the answer, without supporting work, will receive no credit.
Are event A and event B independent? Explain.

(b)

STAT 200: Introduction to Statistics

8.
(a)
(b)

9.

Final Examination, Spring 2016 OL1/US1

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There are 8 books in the “Statistics is Fun” series. (Show all work. Just the answer, without
supporting work, will receive no credit).
How many different ways can Mimi arrange the 8 books in her book shelf?
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?

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
P(x)

-2
0.1

0
0.2

1
0.3

3
0.1

5
0.3

10.

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her
opponent’s serves. Assume her opponent serves 10 times.

(a)

Let X be the number of returns 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?
Find the probability that that she returns at least 1 of the 10 serves from her opponent. Show all
work. Just the answer, without supporting work, will receive no credit.

(b)

11.

Assume the weights of men are normally distributed with a mean of 172 lb and a standard
deviation of 30 lb. Show all work. Just the answer, without supporting work, will receive no
credit.

(a)
(b)

Find the 80th percentile for the distribution of men’s weights.
What is the probability that a randomly selected man is greater than 185 lb?

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 supporting work, will receive no credit.

(a)
(b)

If a random sample of 25 adults is selected, what is the standard deviation of the sample mean?
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.

STAT 200: Introduction to Statistics

Final Examination, Spring 2016 OL1/US1

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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 supporting work, will receive no credit.

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)
(b)
(c)
(d)

16.

Identify the null hypothesis and the alternative hypothesis.
Determine the test statistic. Show all work; writing the correct test statistic, without supporting
work, will receive no credit.
Determine the P-value for this test. Show all work; writing the correct P-value, without
supporting work, will receive no credit.
Is there sufficient evidence to support the claim that more than 75% of the adults believe in
global warming? Explain.
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.

Subject
1
2
3
4
5

Number of Words Recalled
1 hour later 24 hours later
14
12
18
15
11
9
13
12
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.
(a)
(b)
(c)
(d)

Identify the null hypothesis and the alternative hypothesis.
Determine the test statistic. Show all work; writing the correct test statistic, without supporting
work, will receive no credit.
Determine the P-value for this test. Show all work; writing the correct P-value, without
supporting work, will receive no credit.
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.

STAT 200: Introduction to Statistics

17.

(c)
(d)

18.

Brown
42

Yellow
21

(b)

19.

Orange
12

Green
7

Tan
18

Identify the null hypothesis and the alternative hypothesis.
Determine the test statistic. Show all work; writing the correct test statistic, without supporting
work, will receive no credit.
Determine the P-value. Show all work; writing the correct P-value, without supporting work,
will receive no credit.
Is there sufficient evidence to support the claim that the published color distribution is correct?
Justify your answer.

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
y

(a)

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The UMUC Daily News reported that the color distribution for plain M&M’s was: 40% brown,
20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample
of 100 plain M&M’s was classified according to color, and the results are listed below. Use a
0.05 significance level to test the claim that the published color distribution is correct. Show all
work and justify your answer.
Color
Number

(a)
(b)

Final Examination, Spring 2016 OL1/US1

0
1

1
2

2
4

5
8

Find an equation of the least squares regression line. Show all work; writing the correct
equation, without supporting work, will receive no credit.
Based on the equation from part (a), what is the predicted value of y if x = 3? Show all work
and justify your answer.

A farmer is interested in whether there is any variation in the weights of apples between two
trees. Data collected from the two trees are as follows:

Her null hypothesis and alternative hypothesis are:

(a)

Determine the test statistic. Show all work; writing the correct test statistic, without
supporting work, will receive no credit.

STAT 200: Introduction to Statistics

(b)
(c)

Final Examination, Spring 2016 OL1/US1

Page 7 of 7

Determine the P-value for this test. Show all work; writing the correct P-value, without
supporting work, will receive no credit.
Is there sufficient evidence to justify the rejection of H 0 at the significance level of 0.05?
Explain.

20. A study of 5 different weight loss programs involved 250 subjects. Each program was followed by
50 subjects 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 5 programs.
(a)

Complete the following ANOVA table with sum of squares, degrees of freedom, and mean
square (Show all work):
Source of
Variation
Factor
(Between)
Error
(Within)
Total

(b)
(c)
(d)

Sum of Squares
(SS)

Degrees of
Freedom (df)

Mean Square
(MS)

42.36

1100.76

249

Determine the test statistic. Show all work; writing the correct test statistic, without supporting
work, will receive no credit.
Determine the P-value for this test. Show all work; writing the correct P-value, without
supporting work, will receive no credit.
Is there sufficient evidence to support the claim that the mean weight loss is the same for the 5
programs at the significance level of 0.01? Explain.