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STAT 200 Quiz 2
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1. (10 points) Once upon a time, I had a fast-food lunch with a mathematician colleague.
I
noticed a very strange behavior in him. I called it the Au-Burger Syndrome since it was
discovered by me at a burger joint. Based on my unscientific survey, it is a rare but real
malady
inflicting 2% of mathematicians worldwide. Yours truly has recently discovered a
screening test
for this rare malady, and the finding has just been reported to the International
Association of
Insane Scientists (IAIS) for publication. Unfortunately, my esteemed colleagues who
reviewed
my submitted draft discovered that the reliability of this screening test is only 80%. What
it
means is that it gives a positive result, false positive, in 20% of the mathematicians tested
even
though they are not afflicted by this horribly-embarrassing malady.
I have found an unsuspecting victim, oops, I mean subject, down the street. This good old
mathematician is tested positive! What is the probability that he is actually inflicted by
this rare
disabling malady?
2. (5 points) Most of us love Luzon mangoes, but hate buying those that are picked too
early. Unfortunately, by waiting until the mangos are almost ripe to pick carries a risk of
having
15% of the picked rot upon arrival at the packing facility. If the packing process is all
done by
machines without human inspection to pick out any rotten mangos, what would be the
probability of having at most 2 rotten mangos packed in a box of 12?
3. (5 points) We have 7 boys and 3 girls in our church choir. There is an upcoming
concert in
the local town hall. Unfortunately, we can only have 5 youths in this performance. This
performance team of 5 has to be picked randomly from the crew of 7 boys and 3 girls.
a. What is the probability that all 3 girls are picked in this team of 5?
b. What is the probability that none of the girls are picked in this team of 5?

c. What is the probability that 2 of the girls are picked in this team of 5?
4. (10 points) In this economically challenging time, yours truly, CEO of the Outrageous
Products Enterprise, would like to make extra money to support his frequent filet-
mignon-anddouble-lobster-tail
dinner habit. A promising enterprise is to mass-produce tourmaline wedding
rings for brides. Based on my diligent research, I have found out that women's ring size
normally distributed with a mean of 6.0, and a standard deviation of 1.0. I am going to
order
5000 tourmaline wedding rings from my reliable Siberian source. They will manufacture
ring
size from 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, and 9.5. How many wedding
rings
should I order for each of the ring size should I order 5000 rings altogether? (Note: It is
natural to assume that if your ring size falls between two of the above standard
manufacturing
size, you will take the bigger of the two.)
5. (5 points) A soda company want to stimulate sales in this economic climate by giving
customers a chance to win a small prize for ever bottle of soda they buy. There is a 20%
chance
that a customer will find a picture of a dancing banana ( ) at the bottom of the cap upon
opening up a bottle of soda. The customer can then redeem that bottle cap with this
picture for a
small prize. Now, if I buy a 6-pack of soda, what is the probability that I will win
something,
i.e., at least winning a single small prize?
6. (5 points) When constructing a confidence interval for a population with a simple
random
sample selected from a normally distributed population with unknown σ, the Student
tdistribution
should be used. If the standard normal distribution is correctly used instead, how
would the confidence interval be affected?
7. (10 points) Below is a summary of the Quiz 1 for two sections of STAT 225 last
spring. The
questions and possible maximum scores are different in these two sections. We notice
that
Student A4 in Section A and Student B2 in Section B have the same numerical score.
Section A
Student Score
Section B
Student Score
A1 70 B1 15
A2 42 B2 61
A3 53 B3 48

A4 61 B4 90
A5 22 B5 85
A6 87 B6 73
A7 59 B7 48
----- ------ B8 39
How do these two students stand relative to their own classes? And, hence, which student
performed better? Explain your answer.
8. (5 points) My brother wants to estimate the proportion of Canadians who own their
house.
What sample size should be obtained if he wants the estimate to be within 0.02 with 90%
confidence if
a. he uses an estimate of 0.675 from the Canadian Census Bureau?
b. he does not use any prior estimates? But in solving this problem, you are actually using
a
form of "prior" estimate in the formula used. In this case, what is your "actual" prior
estimate? Please explain.
9. (5 points) An amusement park is considering the construction of an artificial cave to
attract
visitors. The proposed cave can only accommodate 36 visitors at one time. In order to
give
everyone a realistic feeling of the cave experience, the entire length of the cave would be
chosen
such that guests can barely stand upright for 98% of the all the visitors.
The mean height of American men is 70 inches with a standard deviation of 2.5 inches.
An
amusement park consultant proposed a height of the cave based on the 36-guest-at-a-time
capacity. Construction will commence very soon.
The park CEO has a second thought at the last minute, and asks yours truly if the
proposed
height is appropriate. What would be the proposed height of the amusement park
consultant? And do you think that it is a good recommendation? If not, what should be
the
appropriate height? Why?
10. (5 points) A department store manager has decided that dress code is necessary for
team
coherence. Team members are required to wear either blue shirts or red shirts. There are
9 men
and 7 women in the team. On a particular day, 5 men wore blue shirts and 4 other wore
red
shirts, whereas 4 women wore blue shirts and 3 others wore red shirt. Apply the Addition
Rule to
determine the probability of finding men or blue shirts in the team.
Please refer to the following information for Question 11 and 12.

It is an open secret that airlines overbook flights, but we have just learned that bookstores
underbook (I might have invented this new term.) textbooks in the good old days that we
had to
purchase textbooks.
To make a long story short, once upon a time, our UMUC designated virtual bookstore,
MBS
Direct, routinely, as a matter of business practice, orders less textbooks than the amount
requested by UMUC's Registrar's Office. That is what I have figured out....... Simply put,
MBS
Direct has to "eat" the books if they are not sold. Do you want to eat the books? You may
want
to cook the books before you eat them! Oops, I hope there is no account major in this
class?
OK, let us cut to the chase..... MBS Direct believes that only 85% of our registered
students
will stay registered in a class long enough to purchase the required textbook. Let's pick on
our
STAT 200 students. According to the Registrar's Office, we have 600 students enrolled in
STAT
200 this spring 2014.
11. (10 points) Suppose you are the CEO of MBS Direct, and you want to perform a
probability
analysis. What would be the number of STAT 200 textbook bundles you would order so
that
you stay below 5% probability of having to back-order from Pearson Custom Publishing?
(Note:
Our Provost would be very angry when she hears that textbook bundles have to be
backordered.
In any case, we no longer need the service of MBS Direct as we are moving to 100% to
free eResources. Auf Wiedersehen, MBS Direct......)
IMPORTANT: Yes, you may use technology for tacking Question 11 in this quiz.
12. (5 points) Is there an approximation method for Question 11? If so, please tackle
Question
11 with the approximation method.
======================================
STAT 200 Week 2 HomeWork

7. For the data from the 1977 Stat. and Biom. 200 class for eye color, construct:
a. pie graph
b. horizontal bar graph
c. vertical bar graph
d. a frequency table with the relative frequency of each eye color
Eye Color
Number of students
Brown
11
Blue
10
Green
4
Gray
1
9. Which of the box plots below has a large positive skew? Which has a large negative
skew?
6. You recorded the time in seconds it took for 8 participants to solve a puzzle. These
times appear below. However, when the data was entered into the statistical program, the
score that was supposed to be 22.1 was entered as 21.2. You had calculated the following
measures of central tendency: the mean, the median, and the mean trimmed 25%. Which
of these measures of central tendency will change when you correct the recording error?
Time (seconds)
15.2
18.8
19.3
19.7
20.2
21.8
22.1
29.4
8. You know the minimum, the maximum, and the 25th, 50th, and 75th percentiles of
a distribution. Which of the following measures of central tendency or variability can you
determine?
mean, median, mode, trimean, geometric mean,range, interquartile range, variance,
standard deviation
30. (AT) What is the mean number of correct responses of the participants after taking
the placebo (0 mg/kg)?

31. (AT) What are the standard deviation and the interquartile range of the d0 condition?
78. Twenty-five randomly selected students were asked the number of movies they
watched the previous week. The results are as follows:
# of movies Frequency Relative Frequency Cumulative Relative Frequency
0 5
1 9
2 6
3 4
4 1
80. If the data were collected by asking the first 111 people who entered the store, then
the type of sampling is:
a. Cluster
b. Simple random
c. stratified
d. convenience
84. Given the following box plot:
Figure 2.41
a. Which quarter has the smallest spread of data? What is that spread?
b. Which quarter has the largest spread of data? What is that spread?
c. Find the interquartile range (IQR).
d. Are there more data in the interval 5–10 or in the interval 10–13? How do you
know this?
e. Which interval has the fewest data in it? How do you know this?
i. 0–2
ii. 2–4
iii. 10–12
iv. 12–13
v. need more information
88. Given the following box plots, answer the questions.
a. In complete sentences, explain why each statement is false.
i. Data 1 has more data values above two than Data 2 has above two.
ii. The data sets cannot have the same mode.
iii. For Data 1, there are more data values below four than there are above four.
b. For which group, Data 1 or Data 2, is the value of “7” more likely to be an outlier?
Explain why in complete sentences.
=====================================

7. You flip a coin three times. (a) What is the probability of getting heads on only one of
your flips? (b) What is the probability of getting heads on at least one flip?
25. You are to participate in an exam for which you had no chance to study, and for that
reason cannot do anything but guess for each question (all questions being of the multiple
choice type, so the chance of guessing the correct answer for each question is 1/d, d being
the number of options (distractors) per question; so in case of a 4-choice question, your
guess chance is 0.25). Your instructor offers you the opportunity to choose amongst the
following exam formats: I. 6 questions of the 4-choice type; you pass when 5 or more
answers are correct; II. 5 questions of the 5-choice type; you pass when 4 or more
answers are correct; III. 4 questions of the 10-choice type; you pass when 3 or more
answers are correct. Rank the three exam formats according to their attractiveness. It
should be clear that the format with the highest probability to pass is the most attractive
format. Which would you choose and why?
27. A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums,
and 2 mangos.
a. Imagine you stick your hand in this refrigerator and pull out a piece of fruit at random.
What is the probability that you will pull out a pear?
b. Imagine now that you put your hand in the refrigerator and pull out a piece of fruit.
You decide you do not want to eat that fruit so you put it back into the refrigerator and
pull out another piece of fruit. What is the probability that the first piece of fruit you pull
out is a banana and the second piece you pull out is an apple?
c. What is the probability that you stick your hand in the refrigerator one time and pull
out a mango or an orange?
86. Roll two fair dice. Each die has six faces.
a. List the sample space.
b. Let A be the event that either a three or four is rolled first, followed by an even
number. Find P(A).
c. Let B be the event that the sum of the two rolls is at most seven. Find P(B).
d. In words, explain what “P(A|B)” represents. Find P(A|B).
e. Are A and B mutually exclusive events? Explain your answer in one to three complete
sentences, including numerical justification.
f. Are A and B independent events? Explain your answer in one to three complete
sentences, including numerical justification.
98. At a college, 72% of courses have final exams and 46% of courses require research
papers. Suppose that 32% of courses have a research paper and a final exam. Let F be the

event that a course has a final exam. Let R be the event that a course requires a research
paper.
a. Find the probability that a course has a final exam or a research project.
b. Find the probability that a course has NEITHER of these two requirements
112. Table 3.22 identifies a group of children by one of four hair colors, and by type of
hair.
Hair TypeBrown Blonde Black Red Totals
Wavy 20 15 3 43
Straight 80 15 12
Totals 20 215
Complete the table.
What is the probability that a randomly selected child will have wavy hair?
What is the probability that a randomly selected child will have either brown or blond
hair?
What is the probability that a randomly selected child will have wavy brown hair?
What is the probability that a randomly selected child will have red hair, given that he or
she has straight hair?
If B is the event of a child having brown hair, find the probability of the complement
of B.
In words, what does the complement of B represent?
124. Suppose that 10,000 U.S. licensed drivers are randomly selected.
a. How many would you expect to be male?
b. Using the table or tree diagram, construct a contingency table of gender versus age
group.
c. Using the contingency table, find the probability that out of the age 20–64 group, a
randomly selected driver is female.
72. You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100
tickets available to be sold in this lottery. In this lottery there are one $500 prize, two
$100 prizes, and four $25 prizes. Find your expected gain or loss.
80. Florida State University has 14 statistics classes scheduled for its Summer 2013 term.
One class has space available for 30 students, eight classes have space for 60 students,
one class has space for 70 students, and four classes have space for 100 students.
a. What is the average class size assuming each class is filled to capacity?
b. Space is available for 980 students. Suppose that each class is filled to capacity and
select a statistics student at random. Let the random variable X equal the size of the
student’s class. Define the PDF for X.
c. Find the mean of X.
d. Find the standard deviation of X.
88. A school newspaper reporter decides to randomly survey 12 students to see if they
will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she

knows that 18% of students attend Tet festivities. We are interested in the number of
students who will attend the festivities.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. How many of the 12 students do we expect to attend the festivities?
e. Find the probability that at most four students will attend.
f. Find the probability that more than two students will attend
===============================
8. Assume the speed of vehicles along a stretch of I-10 has an approximately normal
distribution with a mean of 71 mph and a standard deviation of 8 mph. a. The current
speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed
limit? b. What proportion of the vehicles would be going less than 50 mph? c. A new
speed limit will be initiated such that approximately 10% of vehicles will be over the
speed limit. What is the new speed limit based on this criterion? d. In what way do you
think the actual distribution of speeds differs from a normal distribution?
11. A group of students at a school takes a history test. The distribution is normal with a
mean of 25, and a standard deviation of 4. (a) Everyone who scores in the top 30% of the
distribution gets a certificate. What is the lowest score someone can get and still earn a
certificate? (b) The top 5% of the scores get to compete in a statewide history contest.
What is the lowest score someone can get and still go onto compete with the rest of the
state?
60. The patient recovery time from a particular surgical procedure is normally distributed
with a mean of 5.3 days and a standard deviation of 2.1 days. What is the median
recovery time? a. 2.7 b. 5.3 c. 7.4 d. 2.1
66. Height and weight are two measurements used to track a child’s development. The
World Health Organization measures child development by comparing the weights of
children who are the same height and the same gender. In 2009, weights for all 80 cm
girls in the reference population had a mean µ = 10.2 kg and standard deviation σ = 0.8
kg. Weights are normally distributed. X~ N(10.2, 0.8). Calculate the z-scores that
correspond to the following weights and interpret them. a. 11 kg b. 7.9 kg c. 12.2 kg
76. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally
distributed with a mean of 250 feet and a standard deviation of 50 feet. a. If X = distance

in feet for a fly ball, then X ~ _____(___, ____) b. If one fly ball is randomly chosen
from this distribution, what is the probability that this ball traveled fewer than 220 feet?
Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the
probability. Find the probability. c. Find the 80th percentile of the distribution of fly
balls. Sketch the graph, and write the probability statement.
62. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally
distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly
sample 49 fly balls. a. If ¯X = average distance in feet for 49 fly balls, then ¯X ~
_____(___, ____) b. What is the probability that the 49 fly balls traveled an average of
less than 240 feet? Sketch the graph. Scale the horizontal axis ¯X . Shade the region
corresponding to the probability. Find the probability. c. Find the 80th percentile of the
distribution of the average of 49 fly balls.
70. Which of the following is NOT TRUE about the distribution for averages? a. The
mean, median, and mode are equal. b. The area under the curve is one. c. The curve never
touches the x-axis. d. The curve is skewed to the right.
96. A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20
randomly selected adults are given an IQ test, what is the probability that the sample
mean scores will be between 85 and 125 points?
=================================
5. When you construct a 95% confidence interval, what are you 95% confident about?
8. What is the effect of sample size on the width of a confidence interval?
11. A population is known to be normally distributed with a standard deviation of 2.8.
Compute the 95% confidence interval on the mean based on the following sample of
nine:
8, 9, 10, 13, 14, 16, 17, 20, 21.
15. You take a sample of 22 from a population of test scores, and the mean of your
sample is 60. (a) You know the standard deviation of the population is 10. What is the
99% confidence interval on the population mean? (b) Now assume that you do not know
the population standard deviation, but the standard deviation in your sample is 10. What
is the 99% confidence interval on the mean now?
106. Suppose that a committee is studying whether or not there is waste of time in our
judicial system. It is interested in the mean amount of time individuals waste at the
courthouse waiting to be called for jury duty. The committee randomly surveyed 81

people who recently served as jurors. The sample mean wait time was 8 hours with a
sample standard deviation of 4 hours. Construct a 95% confidence interval for the
population mean time wasted.
112. In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a
standard deviation of $3,156. Assume the underlying distribution is approximately
normal. Construct a 95% confidence interval for the population mean cost of a used car.
122. Stanford University conducted a study of whether running is healthy for men and
women over age 50. During the first eight years of the study, 1.5% of the 451 members of
the 50-Plus Fitness Association died. We are interested in the proportion of people over
50 who ran and died in the same eightyear period. Construct a 97% confidence interval
for the population proportion of people over 50 who ran and died in the same eight–year
period.
==============================
Lane Chap. 11
18. You choose an alpha level of .01 and then analyze your data.
a. What is the probability that you will make a Type I error given that the null hypothesis
is true?
b. What is the probability that you will make a Type I error given that the null hypothesis
is false?
Lane Chap.12
13. You are conducting a study to see if students do better when they study all at once or
in intervals. One group of 12 participants took a test after studying for one hour
continuously. The other group of 12 participants took a test after studying for three
twenty minute sessions. The first group had a mean score of 75 and a variance of 120.
The second group had a mean score of 86 and a variance of 100.
a. What is the calculated t value? Are the mean test scores of these two groups
significantly different at the .05 level?
b. What would the t value be if there were only 6 participants in each group? Would the
scores be significant at the .05 level?
Illowsky Chap.9
65. Previously, an organization reported that teenagers spent 4.5 hours per week, on
average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen
randomly chosen teenagers were asked how many hours per week they spend on the

phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0.
Conduct a hypothesis test. The null and alternative hypotheses are:
a. Ho: x ¯ = 4.5,Ha : x ¯ > 4.5
b. Ho:μ≥ 4.5,Ha:μ< 4.5
c. Ho:μ= 4.75,Ha:μ> 4.75
d. Ho:μ= 4.5,Ha:μ> 4.5
71. Previously, an organization reported that teenagers spent 4.5 hours per week, on
average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen
randomly chosen teenagers were asked how many hours per week they spend on the
phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0.
Conduct a hypothesis test, the Type I error is:
a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is
higher
b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is
the same
c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher
d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact,
it is not higher
77. An article in the San Jose Mercury News stated that students in the California state
university system take 4.5years, on average, to finish their undergraduate degrees.
Suppose you believe that the mean time is longer. You conduct a survey of 49 students
and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data
support your claim at the 1% level?
Illowsky Chap.10
80. At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds)
they could hold their breath in a relaxed position. After a two-minute rest, they timed
themselves while jumping. The girls thought that the mean difference between their
jumping and relaxed times would be zero. Test their hypothesis.
91. A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people.
Of interest is whether the liquid diet yields a higher mean weight loss than the powder
diet. The powder diet group had a mean weight loss of 42 pounds with a standard
deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a
standard deviation of 14 pounds.
120. A golf instructor is interested in determining if her new technique for improving
players’ golf scores is effective. She takes four new students. She records their 18-hole
scores before learning the technique and then after having taken her class. She conducts a
hypothesis test. The data are as follows.
The correct decision is:
1. RejectH0.
2. Do not reject the H0.
=================================

Lane Chap. 14
2. The formula for a regression equation is Y’ = 2X + 9.
a. What would be the predicted score for a person scoring 6 on X?
b. If someone’s predicted score was 14, what was this person’s score on X?
6. For the X, Y data below, compute:
a. r and determine if it is significantly different from zero.
b. the slope of the regression line and test if it differs significantly from zero.
c. the 95% confidence interval for the slope.
Lane Chap. 17
5. At a school pep rally, a group of sophomore students organized a free raffle for prizes.
They claim that they put the names of all of the students in the school in the basket and
that they randomly drew 36 names out of this basket. Of the prize winners, 6 were
freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not
seem that random to you. You think it is a little fishy that sophomores organized the raffle
and also won the most prizes. Your school is composed of 30% freshmen, 25%
sophomores, 25% juniors, and 20% seniors.
a. What are the expected frequencies of winners from each class?
b. Conduct a significance test to determine whether the winners of the prizes were
distributed throughout the classes as would be expected based on the percentage of
students in each group. Report your Chi Square and p values.
c. What do you conclude?
14. A geologist collects hand-specimen sized pieces of limestone from a particular area.
A qualitative assessment of both texture and color is made with the following results. Is
there evidence of association between color and texture for these limestones? Explain
your answer.
Illowsky Chap.11
Decide whether the following statements are true or false.
70. The standard deviation of the chi-square distribution is twice the mean. Use the
following information to answer the next exercise: Suppose an airline claims that its
flights are consistently on time with an average delay of at most 15 minutes. It claims that
the average delay is so consistent that the variance is no more than 150 minutes.
Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for
his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard
deviation of 15 minutes.
Illowsky Chap.12

66.Can a coefficient of determination be negative? Why or why not?
The cost of a leading liquid laundry detergent in different sizes is given.
82.Using “size” as the independent variable and “cost” as the dependent variable, draw a
scatter plot.
1. Does it appear from inspection that there is a relationship between the variables?
Why or why not?
2. Calculate the least-squares line. Put the equation in the form of: ŷ=a+bx
3. Find the correlation coefficient. Is it significant?
4. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.
5. If the laundry detergent were sold in a 90-ounce size, find the estimated cost.
6. Does it appear that a line is the best way to fit the data? Why or why not?
7. Are there any outliers in the given data?
8. Is the least-squares line valid for predicting what a 300-ounce size of the laundry
detergent would you cost? Why or why not?
9. What is the slope of the least-squares (best-fit) line? Interpret the slope.
===================================
Lane Chap. 15
10. If an experiment is conducted with 5 conditions and 6 subjects in each condition,
what are dfn and dfe?
17. The following data are from a hypothetical study on the effects of age and time on
scores on a test of reading comprehension. Compute the analysis of variance summary
table.
28. (AT) The dataset ADHD Treatment has four scores per subject.
Is the design between-subjects or within-subjects?
Create an ANOVA summary table.
69. A researcher wants to know if the mean times (in minutes) that people watch their
favorite news station are the same. Suppose that Table 13.24 shows the results of a study.
Assume that all distributions are normal, the four population standard deviations are
approximately the same, and the data were collected independently and randomly. Use a
level of significance of 0.05.
====================================

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