STAT 200 Final Exam (Fall 2015)

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 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, please cite the sources and explain how you get the results.

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1.
True or False. Justify
for full credit.

(a)If the variance of a data set is zero, then all the
observations in this data set are zero. (b)If P(A) = 0.4 , P(B) = 0.5, and A
and B are disjoint, then P(A AND B) = 0.9.

(c)
Assume X follows a continuous distribution which is
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(d)
A 95% confidence interval is wider than a 90%
confidence interval of the same parameter.
(e)
In a right-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) = 0.96, then we fail to reject the null hypothesis at 0.05 level of significance . .gif">

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.

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.

Checkout
Time (in minutes)

Frequency

Relative Frequency

1.0 – 1.9

3

2.0 – 2.9

12

3.0 – 3.9

0.20

4.0 – 4.9

3

5.0 -5.9

Total

25

2.
Complete the frequency table with frequency and
relative frequency. Express the relative frequency to two decimal places.
3.
What percentage of the checkout times was at least
3 minutes?
4.
5.
Does this distribution have positive skew or
negative skew? Why?
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Refer to the following
information for Questions 6 and 7. Show all work. Just the answer, without
supporting work, will receive no credit.

Consider selecting one card at a time from a 52-card deck. (Note: There are 4 aces in a deck of cards)

6.
If the card selection is without replacement, what
is the probability that the first card is an ace and the second card is also an
ace? (Express the answer in simplest
fraction form) (5
pts)
7.
If the card selection is with replacement, what is
the probability that the first card is an ace and
the second card is also an
ace? (Express the answer in simplest
fraction form)
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Refer to the following situation for Questions 8, 9, and
10.

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

Quiz 1

15

45

55

85

100

Quiz 2

20

35

50

90

100

For
each question, give your answer as one of the following: (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. Then

8.
Which quiz has less interquartile range in grade
distribution?
9.
Which quiz has the greater percentage of students
10.
Which quiz has a greater percentage of students

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Refer to the following
information for Questions 11, 12, and 13. Show
all work. Just the answer, without supporting work, will receive no credit.

There are 1000 students in a high school. Among the 1000 students, 800 students have a
laptop, and 300 students have a tablet.
150 students have both devices.

11.
What is the probability that a randomly selected
student has neither device?
12.
What is the probability that a randomly selected
student has a laptop, given that he/she
has a
tablet?
13.
Let event A be the selected student having a
laptop, and event B be the selected student having a tablet. Are A and B
independent events? Why or why not? .gif”>

14.
A combination lock uses three distinctive numbers
between 0 and 49 inclusive. How many
different ways can a sequence of three numbers be selected? (Show work)
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15.
Let random variable x represent the number of heads when a fair coin is tossed three
times. Show all work. Just the answer, without supporting work, will receive
no credit.

(a)
Construct a table describing the probability
distribution.
(b)
Determine the mean and standard deviation of x. (Round the answer to two decimal
places)

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16. 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 work)

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Refer to the following
information for Questions 17, 18, and 19. Show
all work. Just the answer, without supporting work, will receive no credit.

The lengths of mature jalapeño fruits are normally distributed with a
mean of 3 inches and a standard deviation of 1 inch.

17.
What is the probability that a randomly selected
mature jalapeño fruit is between 1.5 and 4 inches long? (5 pts)
18.
Find the 90th percentile of the jalapeño
fruit length distribution.
19.
If a random sample of 100 mature jalapeño fruits is
selected, what is the standard deviation of the sample mean?
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20.
Arandom sample of 100 light bulbs has a mean
lifetime of 3000 hours. Assume that the population standard deviation of the
lifetime is 500 hours. Construct a 95% confidence interval
estimate of the mean lifetime. Show all work. Just the answer, without
supporting work, will
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21. Consider the
hypothesis test given by

H0:p?0.5

H1:p?0.5

In a random
sample of 100 subjects, the sample proportion is found to be pˆ?0.45.

(a)
Determine the test statistic. Show all work; writing the correct test statistic, without supporting
(b)
Determine the P-value
for this test. Show all work; writing the correct P-value, without supporting work,
(c)
Is there sufficient evidence to justify the rejection
of H0
at the ??0.01
level?
Explain.

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22.
Consumption of large amounts of alcohol is known to
increase reaction time. To investigate the effects of small amounts of alcohol,
reaction time was recorded for five individuals before and after the
consumption of 2 ounces of alcohol. Do
the data below suggest that consumption of 2 ounces of alcohol increases mean
reaction time?

Reaction Time (seconds)

Subject

Before After

1

6 7

2

8 8

3

4 6

4

7 8

5

9 8

Assume we want to
use a 0.01 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
(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
consumption of 2 ounces of alcohol increases mean reaction time? Justify your
conclusion.

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23.
The UMUC MiniMart sells four different types of
Halloween candy bags. The manager
reports that the four types are equally popular. Suppose that a sample of 500 purchases yields
observed counts 150, 110, 130, and 110 for types 1, 2, 3, and 4,
respectively.

Type

1

2

3

4

Number of Bags

150

110

130

110

Assume we want to use a 0.10
significance level to test the claim that the four types are equally popular.

(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 the test. Show all work; writing the correct P-value,
without supporting work, will receive no credit.
(d)Is
there sufficient evidence to support the manager’s claim that the four types

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24. 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

0

1

3

5

y

1

2

3

8

(a)
Find an equation of the least squares regression
line. Show all work; writing the correct equation, without supporting work,
(b)
Based on the equation from part (a), what is the
predicted value of y if x = 4?
Show all

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25. A STAT 200 instructor is interested in
whether there is any variation in the final exam grades between her two
classes Data collected from the two
classes are as follows:

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Her null hypothesis and alternative hypothesis are:

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(a)
Determine the test statistic. Show all work; writing the correct test statistic, without supporting