QuizTop of FormQuestion 1 (24 points)Question 1True or Fa.docx

Quiz
Top of Form
Question 1 (24 points)
Question 1:
True or False.
Enter the answer to each of the the questions with:
T for True
F for False
(a) If all the observations in a data set are identical, then the
variance for this data set is zero.
[removed]
(b) If P(A) = 0.4 and P(B) = 0.5, then P(A AND B) = 0.2.
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c. The mean is always equal to the median for a normal
distribution.
[removed]
(
d) A 95% confidence interval is wider than a 90% confidence
interval of the same parameter
.
[removed]
(e) In a two-tailed hypothesis testing at significance level α of
0.05, the test statistic is calculated as 2. If P(X >2) = 0.03, then
we have sufficient evidence to reject the null hypothesis.
[removed]
Bottom of Form
Question 2 options:
Refer to the following frequency distribution for Questions 2, 3,
4, and 5.

Show all work. Just the answer, without supporting work, will
receive no credit.
A random sample of 100 students was chosen from UMUC
STAT 200 classes. The frequency distribution below shows the
distribution for study time each week (in hours).
Checkout Time (in minutes)
Frequency
Relative Frequency
0.0 - 4.9
5
A
5.0 - 9.9
13
B
10.0 - 14.9
C
22
15.0 - 19.9
42
D
20.0 - 24.9
E
F
Total
100
G
Complete the Frequency Table with the missing frequency and
relative frequency numbers.
Enter answer for "A" as a decimal with 2 decimal places with a
zero to the left of the decimal point.
[removed]
Enter answer for "B" as a decimal with 2 decimal places with a

[removed]
Enter answer for "C" as an Integer.
[removed]
Enter answer for "D" as a decimal with 2 decimal places with a
[removed]
Enter answer for "E" as an integer.
[removed]
Enter answer for "F" as a decimal with 2 decimal places with a
[removed]
Question 3 options:
This is the same distribution table from Question 2
Frequency
Relative Frequency
0.0 - 4.9
5
A
5.0 - 9.9
13
B
10.0 - 14.9
C
22
15.0 - 19.9
42
D
20.0 - 24.9

E
F
Total
100
G
What percentage of the study times was at least 15 hours?
Enter answer as a percent without the percent sign to 0 decimal
places.
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Question 4 options:
This is the same distribution table from Question 2
Frequency
Relative Frequency
0.0 - 4.9
5
A
5.0 - 9.9
13
B
10.0 - 14.9
C
22
15.0 - 19.9
42
D
20.0 - 24.9
E
F
Total
100

G
In what class interval must the median lie? Explain your
answer.
Enter answer by selecting the appropriate letter.
a
Interval 1
(0.0 - 4.9)
b Interval 2 (5.0 - 9.9)
c Interval 3 (10.0 - 14.9)
d Interval 4 (15.0 - 19.9)
e Interval 5 (20.0 - 24.9)
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Question 5 options:
This is the same distribution table from Question 2.
Frequency
Relative Frequency
0.0 - 4.9
5
A
5.0 - 9.9
13
B

10.0 - 14.9
C
22
15.0 - 19.9
42
D
20.0 - 24.9
E
F
Total
100
G
The distribution is negatively skewed, symetrical, positively
skewed?
Answer question by entering appropriate letter.
a negatively skewed
b symetrical
c positively skewed
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Question 6 options:
A fair 6-faced die is rolled two times. Let A be the event that
the outcome of the first roll is a multiple of 3, and B be the
event that the outcome of second roll is greater than 4.
How many outcomes are there in the sample space?
Enter answer as an Integer.
[removed]
Question 7 options:
A 6-faced die is rolled two times. Let A be the event that the
outcome of the first roll is an even number, and B be the event
that the outcome of the second roll is greater than 4.

What is the probability that the outcome of the second roll is
greater than 4, given that the first roll is an even number?
Enter answer as a reduced fraction or a decimal rounded to 2
decimal places.
[removed]
Question 8 options:
A fair 6-faced die is rolled two times. Let A be the event that
the outcome of the first roll is a multiple of 3, and B be the
event that the outcome of second roll is greater than 4.
Are
A
and
B
independent?
Enter answer by selecting the appropriate letter.
a Yes The events are independant
b No
The events are dependant
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Question 9 options:
The 5 number summary below shows the grade distribution of
two Stat 200 quizzes.
Minimum
Q1
Median
Q3
Maximum
Quiz 1

12
40
60
95
100
Quiz 2
20
35
50
90
100
Which quiz has less interquartile range in grade distribution?
a Quiz 1
b Quiz 2
c Both quizzes have the same value requested.
d It is impossible to tell using only the given information.
Answer the question by keying in the appropriate letter.
[removed]
Question 10 options:
Minimum
Q1
Median
Q3
Maximum
Quiz 1
12
40
60
95
100
Quiz 2

20
35
50
90
100
Which quiz has the greater percentage of students with grades
of 90 or over?
a Quiz 1
b Quiz 2
[removed]
Minimum
Q1
Median
Q3
Maximum
Quiz 1
12
40
60
95
100
Quiz 2
20
35
50
90
100

Which quiz has lthe greatest number of students with grades
less than 60?
a Quiz 1
b Quiz 2
[removed]
There are 1000 juniors in a college.
Among the 1000 juniors
300 students are taking STAT200
150 students are taking PSYC300
There are 50 students taking both courses.
What is the probability that a randomly selected junior is taking
at least one of these two courses?
Enter answer as a 2 place decimal or a reduced fraction.
[removed]
There are 1000 juniors in a college.
Among the 1000 juniors
300 students are taking STAT200
150 students are taking PSYC300
There are 50 students taking both courses.
What is the probability that a randomly selected junior is taking
PSYC300, given that she is taking STAT200?
Enter answer as a 2 place decimal with a zero to the left of the
decimal point or a reduced fraction.
[removed]
There are 8 books in the "Statistic is Fun" series. Mimi would

like to choose 2 books from the series for her summer reading.
How many different ways can the two books be selected?
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Let random variable x represent the number of girls in a family
of three children.
Construct a table describing the probability distribution.
(You can assume the probability of having a female child is .5
and the gender of each children is independant of each of the
others.)
x
P(x)
0
A
1
B
2
C
3
D
Enter the probability of "A" as a reduced fraction or a 3 place
decimal.
[removed]
Enter the probability of "B" as a reduced fraction or a 3 place
decimal.
[removed]
Enter the probability of "C" as a reduced fraction or a 3 place
decimal.
[removed]
Enter the probability of "D" as a reduced fraction or a 3 place

decimal.
[removed]
Determine the mean and standard deviation of x.
Enter the mean as a 1 place decimal and the standard deviation
rounded to 2 decimal places in the order asked for.
[removed]
[removed]
Rabbits like to eat the cucumbers in Mimi’s garden. There are
10 cucumbers in her
garden which will be ready to harvest in about 10 days.
Based on her experience, the probability
of a cucumber being eaten by the rabbits before harvest is 0.60.
Let X be the number of cucumbers that Mimi harvests (that is,
the number of cucumbers
not eaten
by rabbits). 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?
Enter number of trials as an integer and probabilities as a 1
decimal with
1 place precision with a 0 to the left of the decimal point.
[removed]
[removed]
[removed]
Find the probability that Mimi harvests at least 2 of the 10
cucumber

s.
Enter answer rounded to 3 decimal places.
Do not enter answer as a percent.
[removed]
How many cucumbers can she expect to harvest?
Enter answer with 0 decimal places. (integer)
[removed]
The heights of pecan trees are normaily distributed with a mean
of 10 feet and a standard deviation of 2 feet.
What is the probability that a randomly selected pecan tree is
between 9 and 12 feet tall.
Enter answer as a decimal rounded to 4 decimal places with a 0
to the left of the decimal point.
Do not enter answer as a percent.
[removed]
Find the 80th percentile of the pecan tree height distribution.
Enter answer as a decimal rounded to 1 decimal place.
[removed]
If a random sample of of 225 pecan trees is selected, what is the
standard deviation of the sample mean,

Enter answer as a 2 place decimal or a reduced fraction,
[removed]
Arandom sample of 100 SAT scores has a sample mean of 1500
hours.
Assume that the statistic scores have a population standard
deviation of 300 hours.
Construct a 95% confidence interval estimate of the mean SAT
scores.
Enter the lower and upper confidence limit numbers rounded to
1 decimal place.
Enter the lower confidence interval number first and then the
upper confidence interval number.
[removed]
[removed]
Consider the hypothesis test given by
H
o
: p = 0.5
H
1
: p < 0.5
In a random sample of 100 subjects, the sample proportion is
found to be phat = 0.47
What is the appropriate distribution for performing the
hypothesis test?
a Uniform distribution
b z distribution
c t distribution
d Chi square distribution

e F distribution
Enter appropriate letter for answering this question.
[removed]
Determine the numerical value of the test statistic.
Enter answer rounded to 1 decimal place with a zero to the left
of the decimal point.
[removed]
Determine the
p
-value for this test.
Enter answer rounded to 3 decimal places with a zero to the left
[removed]
Is there sufficient evidence to justify the rejection of Ho at an α
= .01 level?
a Yes: There is sufficient evidence to justify the rejection of
Ho at an α = .01 level
b No: There is insufficient evidence to justify the rejection
of Ho at an α = .01 level
Enter your answer by selecting the appropriate letter.
[removed]
Mimi was curious if regular excise really helps weight loss,
hence she decided to perform a hypothesis test.
A random sample of 5 UMUC students was chosen. The students
took a 30-minute exercise every day for 6 months.
Ther weight for each individual was recorded before and after
the exercise regimen.

Does the data below suggest that the regular exercise helps
weight loss using a 0.01 significance level to test the claim.?
Weight in Pounds
Subjects
Before
After
1
159
130
2
170
160
3
185
180
4
165
165
5
200
190
Identify the null hypothesis and the alternative hypothesis.
a Ho There is no weight loss due to exercising everyday.
Ha Regular daily exercise effects weight loss.
b Ho Regular daily exercise helps weight loss.
Ha There is no weight loss due to exercising everyday.
c Ho There is no weight loss due to exercising everyday.

Ha Regular daily exercise helps weight loss.
Enter the correct answer by selecting the appropriate letter.
[removed]
The appropriate distribution for performing the hypothesis test
is:
a Uniform distribution.
b z distribution
c t distribution
d Chi Square distribution
What is number of degrees of freedom (dF)?
Enter the appropriate letter for selecting the correct distribution
followed by the dF.
Enter 0 for the dF if this is an inappropriate question for the
distribution selected.
[removed]
[removed]
What is the numerical value of the test statistic?
Enter answer rounded to 2 decimal places.
[removed]
What is the numerical value of the Pvalue.
Enter answer rounded to 2 decimal places with a zero to the left
[removed]
Is there sufficient evidence to support the alternate hypothesis?
a There is insufficient evidence to support the alternate
hypothesis.
b There is sufficient evidence to support the alternate
hypothesis.

c There is insufficient evidence to draw any conclusion from
the hypothesis test.
Enter the answer to this question by selecting the appropriate
letter.
[removed]
A Stat 200 instructor is interested in whether there is any
variation in the final grades between her two classes.
Data collected from the two classes are as follows:
Section 1 n
1
= 31 x
1
= 78 s
1
= 10
Section 2 n
2
= 30 x
2
= 72 s
2
= 14
The instructor's null hypothesis and alternative hypothesis are:
H
0:
σ
1
= σ
2
and H
a:
σ
1
< σ

2
is:
b z distribution
c t distribution
e F distribution
Enter the appropriate letter for selecting the correct
distribution.
[removed]
Determine the test statistic for the hypotesis test.
Enter test statistic rounded to 2 decimal places with a zero to
the left of the decimal point.
[removed]
Determine the p-value for this test.
Enter P value rounded to 2 decimal places with a zero to the left
[removed]
Is there sufficient evidence to justify the rejection of the H
0
at the α = .05 level.
a Yes There is sufficient evidence to justify the rejection
of the H
0
b No There is insufficient evidence to justify the rejection
of the H
0

Enter the letter that is appropriate answer for this question.
[removed]
A random sample of 4 professional athletes produced the
following data where x is the number of endorsements a player
has and y is the amount of money made (in millions of dollars).
x
0
1
3
5
y
1
2
3
8
Find the equation of the least squares regression line.
Round each answer to 2 decimal place with the "constant"
followed by the "slope".
[removed]
[removed]
Based on the above equation, what is the predicted value of
y
if
x
= 4?
Round answer to 1 decimal place.

[removed]
The UMUC Daily News reported that the color distribution for
plain M&M's was:
40% brown
20% yellow
20% orange
10% green
10% tan
Each piece of candy in a random sample of 100 plain M&m's
was clasified 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.
Color
Brown
Yellow
Orange
Green
tan
Number
42
21
12
7
18
Identify the null hypothesis by selecting the appropriate letter a
or b.
a The color distribution for plain M&M 's is not in agreement
with what was reported in the UMUC Daily News.
b The color distribution for plain M&M 's is in agreement

[removed]
Identify the alternative hypothesis by selecting the appropriate
letter c or d.
c The color distribution for plain M&M 's is not in agreement
d The color distribution for plain M&M 's is in agreement
[removed]
is:
b z distribution
c t distribution
e F Distribution
What is number of degrees of freedom (dF)?
Enter the appropriate letter for selecting the correct distribution
followed by the dF.
Enter 0 for the dF if this is an inappropriate question for the
distribution selected.
[removed]
[removed]
What is the numerical value of the test statistic?
[removed]
What is the numerical value of the Pvalue?

[removed]
Is there sufficient evidence to support the claim that the
published color distribution is correct??
Enter the appropriate letter for the correct answer.
a The Ho hypothesis is rejected. The Pvalue is less than the
significance level,
b The Ho hypothesis is not rejected. The Pvalue is greater
than than the significance level.
[removed]
Record your answers and work.
Problem Number
Solution
1
(25 pts)
Answers:
(a)
(b)
(c)

(d)
(e)
Work for (a), (b), (c), (d) and (e):
2
(5 pts)
Answer:
Study Time (in hours)
Frequency
Relative Frequency
0.0 – 4.9
5

5.0 - 9.9
13
10.0 - 14.9
0.22
15.0 -19.9
42
20.0 – 24.9
Total
100
Work:
3
(5 pts)
Answer:

Work:
4
(5 pts)
Answer:
Work:
5
(5 pts)
Answer:
Work:
6
(5 pts)
Answer:

Work:
7
(10 pts)
Answer:
Work:
8
(5 pts)
Answer:
Work:
9
(5 pts)
Answer:

Work:
10
(5 pts)
Answer:
Work:
11
(5 pts)
Answer:
Work:
12
(10 pts)
Answer:

Work:
13
(10 pts)
Answer:
Work:
14
(5 pts)
Answer:
Work:

15
(15 pts)
Answer:
(a)
x
P(x)
0
1
2
3
(b) mean = __________ , and standard deviation =
_____________
Work for (a) and (b):

16
(20 pts)
Answer:
(a)
(b)
(c)
Work for (a), (b) and (c) :

17
(10 pts)
Answer:
Work:
18
(5 pts)
Answer:
Work:

19
(5 pts)
Answer:
Work:
20
(10 pts)
Answer:
Work:
21

(15 pts)
Answer:
(a)
(b)
(c)
Work for (a), (b) and (c):
22
(20 pts)
Answer:

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

23
(10 pts)
Answer:
(a)
(b)
(c)
Work for (a), (b) and (c):
24
(20 pts)
Answer:

(a)
(b)
Work for (a) and (b):
25
(15 pts)

Answers:
(a)
(b)
(c)
(d)
Work for (b) and (c):

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