UMUC STAT200 final exam latest 2015 spring december
STAT 200
OL1/US1 Sections
Final Exam
Fall 2015
The final exam will be posted at 12:01 am on October 9, and
it is due at 11:59 pm on October 11, 2015.
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.
Answer all 25 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 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.
Record your answers and work on the separate answer sheet
provided.
This exam has 200 total points.
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. (15
pts)
(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 symmetric about 0. If
, then .
(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 Studentâs t-distribution with P(T < 1.5) = 0.96, then we
fail to reject the null hypothesis at 0.05 level of significance .
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. (5 pts)
3. What
percentage of the checkout times was at least 3 minutes? (3 pts)
4. In what
class interval must the median lie?
Explain your answer. (5 pts)
5. Does this
distribution have positive skew or negative skew? Why? (2 pts)
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) (5
pts)
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
explain
your answer in each case. (4
pts each)
8. Which
quiz has less interquartile range in grade distribution?
9. Which
quiz has the greater percentage of students with grades 90 and over?
10. Which quiz
has a greater percentage of students with grades less than 60?
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? (10 pts)
12. What is
the probability that a randomly selected student has a laptop, given that
he/she
has a
tablet? (5
pts)
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? (5
pts)
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) (5 pts)
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. (5
pts)
(b) Determine
the mean and standard deviation of x. (Round the answer to two decimal places)
(10
pts)
16. Mimi just
started her tennis class three weeks ago. On average, she is able to return 20%
of her opponentâs 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? (5
pts)
(b) Find the
probability that that she returns at least 1 of the 10 serves from her
opponent.
(Show
work) (10
pts)
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. (5
pts)
19. If a
random sample of 100 mature jalapeño fruits is selected, what is the standard
deviation of the sample mean? (5
pts)
20. A random
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
receive
no credit. (8
pts)
2 1. 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 pË ? 0.45.
(a) Determine
the test statistic. Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(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 ??0.01 level?
Explain.
(15
pts)
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 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 consumption of 2 ounces of
alcohol increases mean reaction time? Justify your conclusion.
(15
pts)
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 managerâs claim that the four types are
equally popular? Justify your answer.
(15 pts)
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,
will receive no credit. (10
pts)
(b) Based on
the equation from part (a), what is the predicted value of y if x = 4? Show all
work
and justify your answer. (5
pts)
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:
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.
(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 significance level of
0.05?
Explain.
(10
pts)
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