STAT 200 Introduction to Statistics Final Examination, Spring 2016 OL2

STAT 200: Introduction to Statistics

Final Examination, Spring 2016 OL2

Page 1 of 7

STAT 200
OL2 Sections
Final Exam
Spring 2016
The final exam will be posted at 12:01 am on March 25, and it is
due at 11:59 pm on March 27, 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 OL2

Page 2 of 7

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

If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A OR B) = 0.9.
If the variance of a data set is zero, then all the observations in this data set are zero.
The mean is always equal to the median for a normal distribution.
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 100th
product from the assembly line.
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.
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.
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.

(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)

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?

STAT 200: Introduction to Statistics

Final Examination, Spring 2016 OL2

Page 3 of 7

(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
Quiz 1
Quiz 2

Q1

Median

Q3

Maximum

15
20

35
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 85 and over?
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)
(b)

List all outcomes in the sample space.
What is the probability that neither marble is red?
fraction form)

6.

There are 1000 students in a high school. Among the 1000 students, 200 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)
(b)

Provide a written description of the complement event of (S OR F).
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.
Are event A and event B independent? Explain.

(b)

(Express the answer in simplest

STAT 200: Introduction to Statistics

8.
(a)
(b)

9.

Final Examination, Spring 2016 OL2

Page 4 of 7

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 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 supporting work, will receive no credit.

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 90th 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 OL2

Page 5 of 7

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)

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.

STAT 200: Introduction to Statistics

Final Examination, Spring 2016 OL2

Page 6 of 7

(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.

(a)
(b)
(c)
(d)

18.

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..
Identify the null hypothesis and 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 researcher’s claim? Explain.

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)
(c)
(d)

19.

Brown
42

Yellow
21

(b)

Green
11

Tan
14

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)

Orange
12

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.

STAT 200: Introduction to Statistics

Final Examination, Spring 2016 OL2

Page 7 of 7

20. A study of 10 different weight loss programs involved 500 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 10 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

N/A

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
10 programs at the significance level of 0.05? Explain