STAT 200: Introduction to Statistics
Final Examination Answers
Follow Below Link to Download Tutorial
Email us At: Support@homeworklance.com or lancehomework@gmail.com
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) The standard deviation of
a data set cannot be negative.
(b) If P(A) = 0.4 , P(B) = 0.5, and
A and B are disjoint, then P(A AND B) = 0.2.
(c) The mean is always equal
to the median for a normal distribution.
(d) A 95% confidence interval is
wider than a 98% confidence interval of the same parameter.
(e) 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.
(b) 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.
(c) The quality control department
of a semiconductor manufacturing company tests every 100th product from
the assembly line.
(d) 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.
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
25
(a)
Complete the frequency table with
frequency and relative frequency. Express the relative
frequency to two decimal places.
(b)
What percentage of the checkout times was
at least 4
minutes?
(c) Does this distribution have positive skew or negative skew? Why?
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 at least one
marble is red? (Express the answer in simplest fraction form)
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
20
35
50
90
100
|
Quiz 1
|
15
|
30
|
55
|
85
|
100
|
|
Quiz 2
|
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
interquartile range in grade distribution?
(b) Which quiz has the greater
percentage of students with grades 90 and over? (c) Which quiz has a
greater percentage of students with grades less than 50?
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) Provide a written
description of the event L OR T. (b) What is the probability of event L
OR T?
- 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.
(b) Are event A and event B
independent? Explain.
STAT 200: Introduction to
Statistics Final Examination, Spring 2016
OL1/US1
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).
(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?
- .
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
- x)
0.1
0.2
0.3
0.1
0.3
- 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?
(b) 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.
- 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) Find the
80th percentile for the distribution of men’s weights.
(b) What is the probability
that a randomly selected man is greater than 185 lb?
- 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)
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?
- A survey showed that 80% of
the 1600 adult respondents believe in global warming. Construct a
- 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
Page 5 of 7
- 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.
- 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
supporting work, will receive no
credit.
(d)
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.
Number of Words Recalled
Subject 1 hour later 24
hours later
18
15
11
9
13
12
12
12
|
1
|
14
|
12
|
|
2
|
||
|
3
|
||
|
4
|
||
|
5
|
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)
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
supporting work, will receive no
credit.
(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.
STAT 200: Introduction to
Statistics Final Examination, Spring 2016
OL1/US1
Page 6 of 7
- The UMUC Daily News reported
that the color distribution for plain M&M’s was: 40% brown,
- 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
Brown
Yellow
Orange
Green
Tan
Number
42
21
12
7
18
(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. Show
all work; writing the correct P-value, without supporting work,
will receive no credit.
(d) Is
there sufficient evidence to support the claim that the published color
distribution is correct?
Justify your answer.
- 18. 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).
1
2
4
8
|
x
|
0
|
1
|
2
|
5
|
|
y
|
(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.
- A farmer is
interested in whether there is any variation in the weights of apples
between two 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 Final Examination, Spring 2016
OL1/US1
Page 7 of 7
(b)
Determine the P-value for this
test. Show all work; writing the correct P-value, without
supporting work, will receive no
credit.
(c)
Is there sufficient evidence to justify
the rejection of at the significance level of 0.05?
Explain.
- 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
Sum of Squares
Mean Square
Variation
- SS)
Factor
42.36
Degrees of
Freedom (df)
(MS)
(Between)
Error
(Within)
Total
1100.76
249
(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
supporting work, will receive no
credit.
(d)
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.
No comments:
Post a Comment