STAT 200 OL4 / OL2 Sections Final Exam Fall 2014

1. True
or False. Justify for full credit. (25
pts)

(a) If
there is no linear correlation between two variables, then these two variables
are not related in any way.

STAT200 : Introduction to
Statistics Final Examination, Fall 2014 OL4 /
US2 Page
2 of 6

(b) If
the variance from a data set is zero, then all the observations in this data
set are identical.

(c) P( A
and A)=1, where Ais the
complement of A.

(d) In
a hypothesis testing, if the P-value is less than the significance level ?, we
reject the null hypothesis.

(e) The
volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete
data set.
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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

1.0 – 1.9

2

2.0 – 2.9

12

3.0 – 3.9

2

4.0 – 4.9

4

2.

What percentage of the checkout times was less than 3
minutes?

(5 pts)

3.

In what class interval must the median
lie? Explain your answer.

(5 pts)

4.

Calculate the mean of this frequency distribution.

(5 pts)

5. Calculate
the standard deviation of this frequency distribution. (Round the answer to two
decimal
places) (10
pts)
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Refer to the following data to answer questions 6, 7 and
8. Show all work. Just the answer, without supporting work,
will receive no credit.

A random sample of STAT200 weekly study times in hours is as
follows:

2

15

15

18

40

6.

Find the sample standard deviation. (Round the
answer to two decimal places)

(10 pts)

7.

Find the coefficient of variation.

(5 pts)

8. Are
any of these study times considered unusual based on the Range
Rule of Thumb?
Show work and
explain. (5
pts)
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Refer to the following information for Questions 9, 10 and
11. 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.
Let event A be the first card is an ace, and event B be the second card is an
ace. (Note: There are 4 aces in a deck of cards)

STAT200
: Introduction to Statistics Final Examination, Fall 2014 OL4
/
US2 Page
3 of 6

9. 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) (10
pts)

10. 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)

(10 pts)

11.

Are A and B independent
when the selection is with replacement? Why or why not?

(5 pts)

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

There are 1000 juniors in a college.
Among the 1000 juniors, 200 students are taking STAT200, and 100 students are
taking PSYC300. There are 50 students taking both courses.

12. What
is the probability that a randomly selected junior is taking at least one of
these two

courses? (10
pts)

13. What
is the probability that a randomly selected junior is taking PSYC300, given
that

he/she is taking
STAT200? (10
pts)
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14. UMUC
Stat Club must appoint a president, a vice president, and a treasurer. There
are 10
qualified candidates. How many different ways can the
officers be appointed? (5
pts)
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15. Mimi
has seven books from the Statistics is Fun series. She plans on bringing three
of the seven

books with
her in a road trip. How many different ways can the three books be
selected? (5 pts)
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Questions
16 and 17 involve the random variable x with probability
distribution given below.
Show all
work. Just the answer, without supporting work, will receive no credit.

x

-1

0

1

2

P( x)

0.1

0.3

0.4

0.2

16.

Determine the expected value of x.

(5 pts)

17.

Determine the standard deviation of x. (Round
the answer to two decimal places)

(10 pts)

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Consider the following situation for Questions 18, 19 and
20. Show all work. Just the answer, without supporting
work, will receive no credit.

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 8 times.

18. 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? (5
pts)

STAT200 : Introduction to
Statistics Final Examination, Fall 2014 OL4 / US2

Page 4 of 6

19.

Find the probability that that she returns at least 1 of
the 8 serves from her opponent.

(10 pts)

20.

How many serves can she expect to return?

(5 pts)

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Refer to the following information for Questions 21, 22, and
23. Show all work. Just the answer, without supporting
work, will receive no credit.

The heights of dogwood trees are normally distributed with a
mean of 9 feet and a standard deviation of 3 feet.

21.

What is the probability that a randomly selected dogwood
tree is greater than 12 feet?

(5 pts)

22.

Find the 75th percentile of the dogwood
tree height distribution.

(10 pts)

23. If
a random sample of 36 dogwood trees is selected, what is the probability that
the mean height

of this sample is less than 10
feet? (10
pts)
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24.A
random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that
thepopulation 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 receive no
credit.(15 pts)
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25. Given
a sample size of 100, with sample mean 730 and sample standard deviation 100,
we perform the following hypothesis test at the a = 0.05
level.

H0 : m=750

H1: m¹750

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

(b) Determine
the critical values. Show all work; writing the correct critical value, without
supporting work, will receive no credit.

(c) What is your conclusion of the test? Please
explain. (20
pts)
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26. Consider
the hypothesis test given by

H0 : p=0.5

H1: p<0.5 In a random sample of 225 subjects, the sample proportion is found to be pˆ = 0.51. (a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 5 of 6 (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 H0 at the a = 0.01 level? Explain. (20 pts) .gif">.gif”>.gif”>.gif”>

27. 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

1

14

12

2

18

15

3

11

9

4

13

12

5

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 0.01 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 work, will receive no credit.

(c) Determine
the critical value. Show all work; writing the correct critical 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.

(20 pts)
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Refer to
the following data for Questions 28 and 29.

x

0

-1

3

5

y

3

-2

3

8

28. Find
an equation of the least squares regression line. Show all work;
writing the correct

equation, without supporting work, will receive no credit. (15
pts)

29. Based
on the equation from # 28, what is the predicted value of y if x =
4? Show all work

and justify your answer. (5
pts)
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STAT200 : Introduction to Statistics

Final Examination, Fall 2014 OL4 / US2

Page 6 of 6

30.

The UMUC MiniMart sells four different types of teddy
bears. The manager reports that

the four types are equally popular. Suppose that a sample
of 100 purchases yields

observed counts 30, 24, 22, and 24 for types 1, 2, 3, and
4, respectively.

Type

1

2

3

4

Number

30

24

22

24

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 critical value. Show all work;
writing the correct critical value,

without supporting work, will receive no credit.

(d)

Is there sufficient evidence to support the manager’s
claim that the four types are

equally popular? Justify your answer.

(20 pts)