Download Name: Math 090 - Greg`s PCC Math Page

Name:_____________________
Date: 7/01/2011
STAT 50
Exam 1
Please show ALL your work on the problems below. No more than 1 point will be
given to problems if you only provide the correct answer and insufficient work.
Some formulas you may need:
x
x
n
PA   1  P A
 x  x 
s
n 1
n x 2   x 
2
2

P A  B  P A  PB  P A  B
n(n  1)
P A  B  P A  PB | A
1. (15 points) In order to figure out the percentage of students at PCC who smoke, Greg
asked the students in his stats class and found that 8 out his 33 students smoke.
a) Describe the population
b) Describe the sample
c) Describe (in words) the population parameter
d) Describe (in words) the sample statistic
e) What is the value of the sample statistic?
2. (27 points) Data:
41
35
77
54
41
21
62
For this data, find the
a) mean
b) median
d) midrange
e) range
f) standard deviation
c) mode
g) variance
h) In the context of this problem, are the numbers 35 and 54 far apart? Why or why not?
3. (6 points) Define a random sample and a simple random sample.
4. (3, 5, 5 points) Consider the procedure where you draw a single card from a standard
poker deck. Let A be the event that you draw an Ace.
a) Find P( A)
b) What does your answer in part (a) mean?
c) If you were to repeat this procedure a total of 26,000 times, how many times will an
Ace be drawn?
5. (6 points) A meteorologist has determined that there is a 72% chance that it will be
sunny tomorrow, a 45% chance that it will be windy tomorrow, and a 38% chance that it
will be both sunny and windy tomorrow. Find
a) The probability that it will be windy or sunny tomorrow
b) The probability that it will not be sunny tomorrow
6. (15 points) Suppose you have data that has a normal distribution with mean   52
and standard deviation   4 . Fill in the blanks below:
68% of the data lies between _____ and _____
_____% of the data lies between 44 and 60
99.7% of the data lies between _____ and _____
7. (39 points) A box contains 12 colored balls with numbers on them as shown below.
Consider the procedure where you draw one ball out of the box.
a) Find the sample space.
b) Let B denote the event that you draw a blue ball from the box, let R denote the event
that you draw a red ball from the box, let G denote the event that you draw a green ball
from the box, let Y denote the event that you draw a yellow ball from the box and let E
denote the event that you draw an even numbered ball from the box. Find the following:
R
E
B Y 
E G 
P (G ) 
P(R ) 
P( E  R) 
PE  G  
P( E | G ) 
P(S ) 
c) Are the events E and G disjoint? Why or why not?
d) Are the events E and G independent? Why or why not?
Name:_____________________
Date: 7/08/2011
STAT 50
Exam 2
Please show ALL your work on the problems below. No more than 1 point will be
given to problems if you only provide the correct answer and insufficient work.
1. (24 points) In this problem we are going to analyze the “3rd 12” bet in roulette. Locate
the box labeled “3rd 12” in the picture above. If you place a bet in this box, you will win
if any of the numbers between 25 and 36 (inclusive) come up and you will lose if
anything else comes up. If you win, you will win double your bet and if you lose, you
will lose the amount of your bet. Suppose you decide to bet $25 on the “3rd 12” box. Let
X be the amount of money you will win when making this bet once.
a) Find the probability distribution of X
c) Find the standard deviation of X
d) Explain the meaning of your answer in part (b)
b) Find the expected value of X
2. (2, rest 6 points) Lucy hates her job and as a result often comes home in a bad mood
because of it. It is estimated that on any given day, the probability that Lucy comes home
4
in a bad mood because of her job is . Let X be the number of times Lucy comes home
5
in a bad mood because of her job this work week (Monday through Friday).
a) What is the name for the distribution of the random variable X?
b) List the 6 things you should always list when working with this kind of random
variable
c) What is the probability that Lucy does not come home in a bad mood because of her
job at all this week?
d) What is the probability that Lucy comes home in a bad mood because of her job
exactly 3 times this week?
e) What is the probability that Lucy comes home in a bad mood because of her job at
least once this week?
(this is a continuation of problem 2)
f) How many times do you expect Lucy to come home this week?
g) Explain what your answer in part (d) means
h) Explain what your answer in part (f) means
i) What is the probability that Lucy comes home in a bad mood because of her job at least
3 times this week? (Hint: Rewrite the phrase “at least 3 times” using and, or, or not)
3. (10 points) Consider the procedure where you flip 3 coins one at a time.
a) What is the sample space?
b) Define your own random variable on this procedure
4. (12 points) Back in the ‘80s, the California Lottery was a game where 6 numbers are
drawn out of a group of 49 (the numbers were 1-49). To play this game, you would buy a
ticket where you would pick 6 numbers of your own and if your numbers matched the 6
numbers that were drawn, then you hit the jackpot.
a) How many such tickets are possible?
b) If you buy 20 different tickets, what is your probability of winning the jackpot?
5. (6 points) Suppose you have just rented 4 movies and you are excited to watch them,
but can’t decide which order to watch them in. How many different orders are possible?
6. (18 points) At John’s sandwich shop, sandwiches are ordered by making 3 decisions:
First the customer decides what kind of bread he wants, then he decides the kind of meat
and finally he decides the kind of cheese. At John’s sandwich shop, there are 4 kinds of
bread, 8 kinds of meat and 5 kinds of cheese.
a) How many different sandwiches can be made?
b) How many of these sandwiches contain cheddar cheese (cheddar cheese is one of the
cheese options)?
c) If you were to pick a sandwich at random, what is the probability that it will have
cheddar cheese?
Some formulas you may need:
PA   1  P A
P A  B  P A  PB  P A  B
P A  B  P A  PB | A
P A  B  P A  PB
P A  B  P A  PB
P(at least one)  1  P(none)
n
Pr 
EV     xp(x)
EV    np
n!
(n  r )!
Var 
n
 x
2
Cr 

n!
(n  r )! r!
p( x)   2
 2  npq

 x
  npq
2

p ( x)   2
Name:_____________________
Date: 7/15/2011
STAT 50
Exam 3
Please show ALL your work on the problems below. No more than 1 point will be
given to problems if you only provide the correct answer and insufficient work.
1. (24 points) The average number of cars you see stalled along side the road as you drive
from Los Angeles to Las Vegas is 3.7.
a) What is the probability that on your next trip to Vegas you will see 7 cars stalled along
side the road?
b) What is the probability that on your next trip to Vegas you will see at least one car
stalled along side the road?
c) What is the probability that on your next trip to Vegas you will see between 4 and 6
cars (inclusive) stalled along side the road?
d) What is the probability that on your next trip to Vegas you will see at least 2 cars
stalled along side the road?
2. (6, 4, 6 points) Suppose the random variable X has a uniform distribution on the
interval [9, 14].
a) Find the value of c that makes this a probability distribution
b) Find P ( X  11)
c) Find P(10  X  12)
3. (12 points) Suppose X is a random variable whose density curve is given below.
a) What are the possible values of X?
b) Find P(35  X  8)
4. (6, 10 points) The lengths of pregnancies are normally distributed with a mean of 268
days and a standard deviation of 15 days.
a) If one pregnant woman is randomly selected, find the probability that her length of
pregnancy is less than 260 days.
b) If 25 pregnant women are randomly selected, find the probability that their lengths of
pregnancies have a mean between 260 days and 270 days.
5. (10, 6 points) There is an 80% chance that a prospective employer will check the
educational background of a job applicant. For 100 randomly selected job applicants,
a) find the probability that between 80 and 92 (inclusive) of these applicants have their
educational background checked
b) find the probability that exactly 85 of these applicants have their educational
backgrounds checked
6. (4, 4, 4, 6, 10, 8 points) In order to figure out the percentage of registered voters who
are planning to vote for President Obama in the next election, a statistics student polls
everyone he sees at the Cheesecake Factory and finds that 47 of the 72 registered voters
at Cheesecake will vote for Obama in the next election.
a) What is the population?
b) What is the sample?
c) What is the population parameter? (in words and symbol)
d) What is the best point estimate for the population parameter we are trying to estimate?
e) Find a 97% confidence interval for the percentage of registered voters who plan on
voting for Obama in the next election.
f) What does the 97% in a 97% confidence interval mean?
Some formulas you may need:
PA   1  P A
P A  B  P A  PB  P A  B
P A  B  P A  PB
P(at least one)  1  P(none)
P( X  x) n C x p x q n  x
P( X  x) 
X  X
e   x
x!
X 
  npq
 2  npq
  np
Z
X
n
X 

E  z / 2
pˆ qˆ
n
Name:_____________________
Date: 7/21/2011
STAT 50
Exam 4
Please show ALL your work on the problems below. No more than 1 point will be
given to problems if you only provide the correct answer and insufficient work.
1. (20, 4 points) Stella wants to sell expensive jewelry at a booth at PCC. However,
before she sets up a booth, she wants to know if students at PCC are too broke to buy her
jewelry. So Stella decides she wants to figure out the average amount of money PCC
students bring with them to school. She asked 25 PCC students how much money they
had on them and after collecting all the data, she determined that the average amount of
money these 25 students had on them was $17.34 with a standard deviation of $4.21.
a) Find a 90% confidence interval for the average amount of money all PCC students
bring with them to school.
b) In the context of this problem, explain what the 90% means in a 90% confidence
interval.
2. (24 points) The weights of 100 different M&M’s were measured and have a mean
weight of 0.85 grams with a standard deviation of 0.0518 grams. Construct a 95%
confidence interval for the variance of the weights of all M&M’s.
3. (24 points) Adults were randomly selected for a Newsweek poll. They were asked if
they “favor or oppose using federal tax dollars to fund medical research using stem cells
obtained from human embryos.” Of those polled, 481 were in favor and 401 were
opposed. A politician claims that people don’t really understand the stem cell issue and
their responses to such questions are random responses equivalent to a coin toss. Use a
0.01 significance level to test the claim that the proportion of subjects who respond in
favor is equal to 0.5.
4. (24 points) The Coca-Cola bottling company has developed a new machine that they
claim is much more consistent when it fills cans of Coke. The standard deviation for the
amount of Coke filled in their cans by their older machines is estimated to be about 0.15
ounces. To determine if this new machine is better, the new machine was used to fill 100
cans of Coke. The standard deviation of the amount of Coke in the cans from this sample
is 0.12 ounces. Use a 0.05 significance level to test the claim that the standard deviation
of the amount of Coke filled in their cans by this new machine is less than 0.15 ounces.
5. (24 points) A scientist developed a pill that is supposed to help students become better
at math. To test the pill, a sample of 350 total students who failed the math placement
exam at PCC were selected and divided into 2 groups, a treatment group and a placebo
group. Each of the 350 students is supposed to take one pill everyday and take PreAlgebra. The treatment group consists of 192 people and 134 of them passed PreAlgebra. Of the 158 people in the placebo group, 97 passed Pre-Algebra. Use a 0.05
significance level to determine if people who take this pill have a better chance of passing
Pre-Algebra than those who don’t take the pill.
Some formulas you may need:
E  z / 2
E  t / 2
z 
n  0.25  / 2 
 E 
pˆ qˆ
n
E  z / 2
n  1s 2    n  1s 2
2
2
s
Z
2
R
n
pˆ  p
pq
n
z
Z

t
n
 pˆ 1  pˆ 2    p1  p 2 
pq pq

n1
n2
n
n  1s 2
L
X 
z  
n    /2 
 E 

 R2
X 
s
2 
2 
n
p
x1  x2
n1  n2
n  1s 2
(n  1) s 2
2
q  1 p
2
 L2
Name:_____________________
Date: 7/28/2011
STAT 50
Exam 5
Please show ALL your work on the problems below. No more than 1 point will be
given to problems if you only provide the correct answer and insufficient work.
1. (24 points) A new weight loss pill has come on the market the company that
manufactures it claims that you can eat anything you want all day long as long as you
take one of these pills a day right before you go to sleep. The company claims that you
will see the loss in 30 days. 700 people volunteered to do a double blind experiment to
test if the drug really works or not. The subjects were randomly selected to be in either
the treatment group or in the placebo group. Over the course of 30 days, the 382 members
of the treatment group had an average weight loss of 14.8 lbs with a standard deviation of
6.4 lbs, while the 318 members of the placebo group had an average weight loss of 4.9
lbs with a standard deviation of 5.9 lbs. Use a hypothesis test at the 0.05 significance
level to test the claim that people who take this diet pill have a mean weight loss higher
than those who don’t and thus that the pill actually works.
2. (24 points) Some people claim that Diet Coke contains a chemical that makes people
have to pee much quicker than if they drink regular Coke. To test this claim, Greg had
some of his students drink a can of Diet Coke after class and timed how long it took them
to have to use the restroom. This experiment was repeated on another day with the same
students using Coke instead of Diet Coke. The results are summarized in the table below.
Use a 0.05 significance level to test the claim that Diet Coke makes people have to pee
sooner than regular Coke.
Student Name
Time it took to use the restroom (Diet Coke)
Time it took to use the restroom (Coke)
Karen
7 min
15 min
Upa
18 min
21 min
Laura
3 min
2 min
Camille
9 min
12 min
Doug
16 min
16 min
3. (24 points) These days it seems that most Armenian women get married around 18
years old whereas Armenian men get married at all sorts of ages. In a simple random
sample of 30 Armenian women, the average age at which they got married (for the first
time) was 19.3 years old with a standard deviation of 1.1 years old. In another simple
random sample of Armenian men, the average age at which they got married (for the first
time) was 26.9 years old with a standard deviation of 4.8 years old. Use a 0.05
significance level to test the claim that the ages at which Armenian women get married
(for the first time) vary less that the ages at which Armenian men get married (for the
first time).
4. (6, 10, 10, 6, 6, 10 points) In order to study the relationship between how much people
smoke and how long it takes to develop lung cancer, 10 smokers who already have lung
cancer were asked how many cigarettes they smoke in a day and how old they were when
they first developed lung cancer. The data is summarized below.
No, of cigarettes smoked per day (x)
Age at which they first developed lung cancer (y)
3
68
10
61
16
48
24
44
5
68
18
49
8
59
10
59
In order to facilitate the rest of the calculations, here are some of the calculations already
done for you:
2
 x  118  x  1,742  y  562  y 2  32,192  xy  6,194
a) Find r
b) Use a 0.05 significance level to test the claim that there is a linear relationship between
x and y.
12
54
12
52
c) Find the equation of the least squares regression line for this data
d) Find the best point estimate for the age at which a person who smokes 20 cigarettes
per day is likely to develop lung cancer.
e) Repeat part (d) if your conclusion in part (b) was false.
f) Find a 95% prediction interval for the age at which a person who smokes 20 cigarettes
per day is likely to develop lung cancer.
Some formulas you may need:
z
x1  x2   1   2 
 12
n1
t
x1  x2   1   2 
s 2p
n1

s 2p

 22
 12
n1

 22
n2
n2
s 2p 
n1  1s12  n2  1s22
n1  1  n2  1
df  n1  n2  2
n2
E  t / 2
t
E  z / 2
x1  x2   1   2 
s12 s 22

n1 n2
s 2p
n1

s 2p
n2
df is the smaller of n1  1 and n2  1
E  t / 2
s12 s 22

n1 n 2
t
d  d
sd
E  t / 2
sd
df  n  1
n
n
F
s12
s 22
df1  n1  1
df 2  n2  1
n x 2   x 
2
s
r
b1 

n xy   x  y 

n  x   x 
2
2
se 
2



n2
2
2
 y  x    x  xy
n x    x 
2
b0 
n  x 2   x 
2
 b0  y  b1  xy

yˆ  b1 x  b0
n  y   y 
n xy   x  y 
t
y
nn  1
r
1 r2
n2
2
2
df  n  2
n x 0  x 
1

n n  x 2   x 2
2
E  t / 2 s e 1 


Name:___________________
Date: 6/28/2011
STAT 50
Quiz 1
1. (5 points) In order to determine the percentage of people in California who drink
energy drinks, a Statistics student goes to lunch at Panda Express and asks the first 100
people he sees there if they drink energy drinks or not. Of the people surveyed, 34 of
them said that they do drink energy drinks.
a) Describe the population
b) Describe the sample
c) Describe (in words) the population parameter
d) Describe (in words) the sample statistic
e) What is the value of the sample statistic?
2. (2 points) Explain the difference between stratified sampling and cluster sampling.
3. (3 points) The final exam scores for my last statistics class are below (out of 250).
Make a relative frequency table and relative frequency histogram for the data using
classes of length 25 whose first class starts with 100.
193
238
120
183
218
108
173
244
240
180
162
189
151
141
196
196
205
195
180
159
Name:___________________
Date: 6/29/2011
STAT 50
Quiz 2
Some formulas you may need:
x
x
1. (8 points) Here is some data:
29
s
41
22
n 1
31
29
57
n x 2   x 
2
2
n
26
 x  x 

nn  1
41
For this data, find the
a) mean
b) median
d) midrange
e) range
f) standard deviation
c) mode
g) variance
2. (1 point) Suppose a set of data has a standard deviation of s  0.1 . With that in mind,
are the data points 52 and 55 considered close together, or far apart? Explain why!
3. (1 point) Suppose you know that your data has a normal distribution with a mean
  73 and a standard deviation of   8 . Fill in the blank below:
______ % of the data is between the values of 57 and 89
Name:___________________
Date: 6/30/2011
STAT 50
Quiz 3
1. (6 points) A bag contains 8 scrabble letters. The letters in the bag are:
E1
K5 J8
Q10 P3 C3
G2
I1
The procedure is to draw a single letter from the bag without looking in the bag. The
number next to each letter tells you how many points each letter is worth. Let A be the
event that a vowel is drawn, and let B be the event that a letter worth 5 or more points.
a) A
b) B
d) P( A)
e) P(B)
c) S
f) P(S )
2. (2 points) In order for the weatherman to determine if it is going to rain today, he
looked at past records and noticed that out of 1287 days in the past that had all the same
conditions as today has, it has rained on 821 of those days. What is the probability that it
rains today?
3. (2 points) Consider the procedure where you draw a single card from a standard deck
1
of 52 poker cards. The probability of drawing a spade is
(or 25%).
4
a) Explain as clearly as possible what this probability means.
b) If you drew a card from the deck, then replaced the card back into the deck, shuffled
and drew a card again and continued this 40,000 times, how many times would you draw
a spade?
Name:___________________
Date: 7/05/2011
Some formulas you may need:
P( A  B)  P( A)  P( B)
STAT 50
Quiz 4
P( A  B)  P( A)  P( B | A)
P(at least one)  1  P(none)
1. (1, 1, 2, 1, 1, 1 points) An unprepared student is about to take a 5 question multiple
choice exam in his stats class. Each of the 5 questions contains 3 choices and only one of
the choices is the correct answer. Since the student has not studied, he is going to guess
the answer to each question at random.
a) What is the probability that the student answers the first question correctly
b) What is the probability that the student answers the first question incorrectly
c) Let I 1 be the event that the student answers the first question incorrectly and let I 2 be
the event that the student answers the second question incorrectly. Are the events I 1 and
I 2 independent? Why or why not?
d) What is the notation for the probability that the student gets all 5 questions on the test
incorrect (use the same notation from part (c) ( I 1 , I 2 , I 3 and so forth)).
e) What is the probability that the student gets all 5 of the questions on the test incorrect?
f) What is the probability that the student gets at least on question correct?
2. (2, 1 points) Consider the procedure where you draw 7 cards from a standard poker
deck one at a time without replacement.
a) What is the probability that you do not draw a single spade?
b) What is the probability that you draw at least one spade?
Name:___________________
Date: 7/06/2011
STAT 50
Quiz 5
Some formulas you may need:
n
Pr 
n!
(n  r )!
n
Cr 
n!
(n  r )! r!
1. (2, 1 points)
a) How many samples of size 5 can be constructed out of a population consisting of 43
members?
b) Suppose you want to select a SIMPLE RANDOM SAMPLE of size 5 from a
population of 43 people. What is the probability that a given sample will be selected?
2. (2, 1 points) In horse racing, betting a trifecta means picking which horse will come in
first, which will come in second, and which will come in third in the correct order.
a) How many different trifecta bets are possible in a 9 horse race?
b) If you make 7 trifecta bets in a 9 horse race, what is the probability that you will win
one of these bets?
3. (2 points) How many 7 character license plates are there where the 2nd, 3rd and 4th
characters are letters (A-Z), the rest of the characters are numbers (0-9), and no letter can
be used more than once (but the numbers can repeat).
4. (2 points) A husband, wife, their baby boy and their dog go to a picture place to have
their family photo taken. The photographer insists on lining the 4 up in a straight line, but
is having trouble arranging them in a way that will give the best looking photo. So he
takes one picture for every possible arrangement to make sure he hasn’t overlooked a
good arrangement. How many photos did the photographer take?
Name:___________________
Date: 7/07/2011
STAT 50
Quiz 6
Some formulas you may need:
EV     xp(x)
Var 
 x
2

p( x)   2

 x
2

p ( x)   2
1. (6 points) In this problem, we are going to analyze the field bet in craps. The game of
craps is played by rolling a pair of dice and observing the total of the two numbers on the
dice. Locate the section in the picture above labeled FIELD. When you bet on the field,
the die are rolled once and you will win if any of the totals 2, 3, 4, 9, 10, 11, or 12 are
rolled and you will lose if any other total is rolled. More specifically, you will win the
amount of your wager (you will win $5 if you bet $5) if you roll a 3, 4, 9, 10, or 11.
Notice that the numbers 2 and 12 are circled. That’s because you win more if those totals
are rolled. If you roll total of 2, you will win double your wager and if you roll a 12, you
will triple your wager. Suppose you bet $100 on the field and let the random variable X
be the amount of money you will win on a single roll of the dice.
a) Find the probability distribution for X. (Hint: When finding P( X  100) , there are lots
of ways for X to equal 100. Make sure to count them all)
(problem 1 continued)
b) Find the expected value of X.
c) Find the standard deviation of X.
e) Explain in words the meaning of your answer in part (b).
f) Is this a good bet to make? Why or why not?
2. (2 points) Consider the procedure of drawing a single card from a poker deck. Define a
random variable X on this procedure.
3. (2 points) What are the requirements of a probability distribution?
Name:___________________
Date: 7/11/2011
STAT 50
Quiz 7
Some formulas you may need:
P A  B  P A  PB
e   x
P( X  x) 
x!
P A  B  P A  PB  P A  B
2 
 
1. (1, 1, 1, 1, 1, 2, 3 points) The average number of earthquakes in California in one year
that are over magnitude 3.0 is 78. Let X be the number of earthquakes in California in one
year that are over 3.0 in magnitude.
a) What is the name for the distribution of X?
b) What are the possible values of X?
c) What is the mean of X?
d) What is the variance of X?
e) What is the standard deviation of X?
f) What is the probability that there will be 80 earthquakes in California over magnitude
3.0 next year?
g) What is the probability that there will be between 77 and 80 (inclusive) earthquakes in
California over magnitude next year?
Name:___________________
Date: 7/12/2011
STAT 50
Quiz 8A,B
1. (1, 1, 1, 2, 2, 2, 1 points) Suppose Z has a standard normal distribution.
a) What are the possible values for Z?
b) What is the mean  of Z?
c) What is the standard deviation  of Z?
d) What is P( Z  1.52) ?
e) What is P ( Z  0.42) ?
f) What is P(1.71  Z  0.88) ?
g) What is P ( Z  0.63) ?
2. (2 points) State the requirements for a density curve.
3. (2 points) Suppose X is a random variable with the density curve drawn below.
a) What are the possible values of X?
b) What is P(1  X  7) ?
4. (2 points) Suppose X is uniformly distributed over the interval [3,13].
a) Find c that makes this a probability density.
b) Find P(0  X  7)
5. (4 points) Suppose the heights of 40 year old males is normally distributed with a mean
of 70 inches and a standard deviation of 6 inches. What is the probability that a randomly
selected 40 year old man’s height is between 64 inches and 76 inches? (Hint: Let X
denote the height of a 40 year old male)
Name:___________________
Date: 7/13/2011
STAT 50
Quiz 9
1. (1, 1, 2 points)
a) What kind of object is the population parameter  ?
b) What kind of object is the sample statistic x ?
c) Fill in the blanks: Since EV (x )   , x is an _______________ _______________
of  .
2. (4 points) State the Central Limit Theorem
3. (2 points) Consider the procedure where you roll a pair of dice and let X denote the
average of the two numbers rolled on the dice. Find P( X  4.5)
Name:___________________
Date: 7/14/2011
Some formulas you may need:  X   X
STAT 50
Quiz 10
X 
X
n
  np
  npq
1. (2, 2, 1 points) The Coca-Cola company uses machines to fill their coke cans. The
machines are set to fill the cans with 12 ounces of Coke but for various reasons, some
cans get less than 12 ounces and some get more than 12 ounces. In fact, the amount of
Coke in a can is normally distributed with a mean of 12 ounces and a standard deviation
of 0.2 ounces.
a) If one can of Coke is randomly selected, what is the probability that the amount of
Coke in the can is less than 11.9 ounces?
b) If 64 cans of Coke are randomly selected, what is the probability that the mean amount
of Coke in the 64 cans is less than 11.9 ounces?
c) If the amount of Coke in one can did not have a normal distribution, could part (b) be
done in the same way? Explain as clearly as possible why or why not.
2. (2, 3 points) A gambler is about to play the game of Roulette 300 times, each time
betting on red.
a) Find the probability that the gambler wins at least 120 times
b) Find the probability that the gambles wins between 135 times and 161 times.
Name:___________________
Date: 7/18/2011
Some formulas you may need:
STAT 50
Quiz 11
E  z / 2

n
z  
n    /2 
 E 
2
1. (2, 5, 3 points) A simple random sample of 50 adults (including males and females) is
obtained, and each person’s red blood cell count (in cells per microliter) is measured. The
sample mean is 4.63. The population standard deviation for red blood cell counts is 0.54.
a) Find the best point estimate of the mean red blood cell count of all adults
b) Construct a 99% confidence interval estimate of the mean red blood cell count of
adults.
c) What is the minimum sample size necessary so that the margin of error for a 99%
confidence interval is 0.1?
Name:___________________
Date: 7/19/2011
STAT 50
Quiz 12
Some formulas you may need:
E  t / 2
s
n
n  1s 2    n  1s 2
2
2
R
L
n  1s 2
 R2
2 
n  1s 2
 L2
1. (1, 4, 1, 4 points) In a test of the Atkins weight loss program, 40 individuals
participated in a randomized trial with overweight adults. After 12 months, the mean
weight loss was found to be 2.1 lb, with a standard deviation of 4.8 lb.
a) What is the best point estimate of the mean weight loss of all overweight adults who
follow the Atkins program?
b) Construct a 99% confidence interval estimate of the mean weight loss for all such
subjects
(this is a continuation of problem 1)
c) What is the best point estimate of the standard deviation of the amount of weight loss
of all overweight adults who follow the Atkins program?
d) Construct a 95% confidence interval estimate of the standard deviation of the amount
of weight loss for all such subjects
Name:___________________
Date: 7/20/2011
A formula you may need:
STAT 50
Quiz 13
z
pˆ  p
pq
n
1. (5 points) Cheating Gas Pumps When testing gas pumps in Michigan for accuracy,
fuel-quality enforcement specialists tested pumps and found that 1299 of them were not
pumping accurately (accurately means within 3.3 oz when 5 gallons are pumped), and
5686 pumps were accurate. Use a 0.01 significance level to test the claim of an industry
representative that less than 20% of Michigan gas pumps are inaccurate.
2. (5 points) Driving and Cell Phones In a survey, 1640 out of 2246 randomly selected
adults in the United States said that they use cell phones while driving. Use a 0.05
significance level to test the claim that the proportion of adults who use cell phones while
driving is equal to 75%.
Name:___________________
Date: 7/21/2011
Some formulas you may need:
STAT 50
Quiz 14
z
x

n
x
t
s

2

n  1s 2

2
n
1. (3 points) Weights of Pennies The U.S. mint has a specification that pennies have a
mean weight of 2.5 g. A simple random sample of 37 pennies manufactured after 1983
was taken and those pennies have a mean weight of 2.49910 g and a standard deviation of
0.01648 g. Use a 0.05 significance level to test the claim that this sample is from a
population with a mean weight equal to 2.5 g.
2. (3 points) The Doritos company claims that the average number of chips in their small
bags of chips is 20 chips. A disgruntled consumer claims that Doritos is cheating their
customers and are putting less chips in their bags than they should. To this end, a sample
of 49 bags of chips is obtained and the average number of chips in this sample is 18.3
chips. Suppose that the standard deviation of the number of chips in all Doritos bags is
3.5 chips. Use a 0.01 significance level to test the claim that the mean number of chips in
small Doritos bags is less than 20 chips.
3. (4 points) A can of Coke is supposed to contain 12 oz’s of soda. However, the amount
of soda in each can will vary somewhat. The Coca-Cola company claims that the
standard deviation of the amount of soda in their cans is 0.15 oz’s. To make sure that the
amount of soda in each can is consistent and that their machines used to fill the cans are
working properly, an inspector measures the amount of soda in 49 cans and finds that the
standard deviation of the sample is 0.21 ounces. Test the claim that the standard deviation
of the amount of soda in a can of Coke is larger than 0.15 oz’s at the 0.05 significance
level. Is the Coca-Cola company lying? Do their filling machines need upgrading?
Name:___________________
Date: 7/26/2011
STAT 50
Quiz 15
1. (2, 6, 2 points) A simple random sample of 13 four-cylinder cars is obtained, and the
braking distances are measured. The mean braking distance is 137.5 ft and the standard
deviation is 5.8 ft. A simple random sample of 12 six-cylinder cars is obtained and the
braking distances have a mean of 136.3 ft with a standard deviation of 9.7 ft.
a) Describe the two populations
b) Construct a 90% confidence interval estimate of the difference between the mean
braking distance of four-cylinder cars and the mean breaking distance of six-cylinder cars
c) Use the confidence interval from part (b) to test the claim that the mean braking
distance of four-cylinder cars is greater than the mean breaking distance of six-cylinder
cars at the 0.05 significance level
Some formulas you may need:
z
x1  x2   1   2 
 12
n1
t
x1  x2   1   2 
s 2p
n1

s 2p

 22
 12
n1

 22
n2
n2
s 2p 
n1  1s12  n2  1s22
n1  1  n2  1
df  n1  n2  2
n2
E  t / 2
t
E  z / 2
x1  x2   1   2 
s12 s 22

n1 n2
s 2p
n1

s 2p
n2
df is the smaller of n1  1 and n2  1
E  t / 2
s12 s 22

n1 n 2
Name:___________________
Date: 7/27/2011
STAT 50
Quiz 16
1. (5 points) Is Friday the 13th Unlucky? Researchers collected data on the number of
hospital admissions resulting from motor vehicle crashes, and results are given below for
Fridays on the 6th of a month and Fridays on the following 13th of the same month. Use a
0.05 significance level to test the claim that when the 13th day of a month falls on a
Friday, the number of hospital admissions from motor vehicle crashes is increased.
Friday the 6th:
Friday the 13th:
9
13
6
12
11
14
11
10
3
4
5
12
2. (5 points) Testing Effects of Alcohol Researchers conducted an experiment to test the
effects of alcohol. The errors were recorded in a test of visual and motor skills for a
treatment group of 22 people who drank ethanol and another group of 22 people given a
placebo. The errors for the treatment group have a standard deviation of 2.20, and the
errors from the placebo group have a standard deviation of 0.72. Use a 0.05 significance
level to test the claim that the treatment group has errors that vary more than the errors of
the placebo group.
Some formulas you may need:
t
d  d
sd
E  t / 2
sd
df  n  1
n
n
s12
F 2
s2
df1  n1  1
df 2  n2  1
n x 2   x 
2
s
nn  1
Name:___________________
Date: 7/28/2011
STAT 50
Quiz 17
Some formulas you may need:
r
b1 

n xy   x  y 


n  x 2   x 
n xy   x  y 



yˆ  b1 x  b0
n  y 2   y 
2
n  x 2   x 
2
2
 y  x    x  xy
n x    x 
2
b0 
2
2
1. (4, 4, 2) The data below are blood pressure measurements of 5 patients taken once
from their left arms and once from their right arms (measured in millimeters of Mercury
(mm Hg)). Use x to denote a patient’s right arm blood pressure and let y denote a
patient’s left arm blood pressure.
Right Arm x
Left Arm y
a) Find r
102
175
101
169
94
182
79
146
79
144
b) Find the least squares regression line for the data
c) Use the least squares regression line to predict a patient’s blood pressure in their left
arm if the blood pressure in their right arm is 100 mm Hg.
Name:___________________
Date: 8/2/2011
STAT 50
Quiz 18
Some formulas you may need:
 
2
O  E 2
E
df  k  1
E
n
k
E  pn
1. (5 points) The table below lists the frequency of wins for different post positions in the
Kentucky Derby horse race. A post position of 1 is closest to the inside rail, so that horse
has the shortest distance to run. Use a 0.05 significance level to test the claim that the
likelihood of winning is the same for the different post positions. Based on the results,
should bettors consider the post position of a horse racing in the Kentucky Derby?
Post Position
Wins
1
19
2
14
3
11
4
14
5
14
6
7
7
8
8
11
9
5
10
11
Leading Digit
Benford's Law
distribution of leading
digits
1
30.1%
2
17.6%
3
12.5%
4
9.7%
5
7.9%
6
6.7%
7
5.8%
8
5.1%
9
4.6%
2. (5 points) Amounts of political contributions are randomly selected, and the leading
digits are found to have frequencies of 52, 40, 23, 20, 21, 9, 8, 9, and 30. (Those observed
frequencies correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9 respectively).
Using a 0.01 significance level, test the observed frequencies for goodness-of-fit with
Bedford’s law. Does it appear that the political contributions are legitimate?
Name:___________________
Date: 8/3/2011
STAT 50
Quiz 19
Some formulas you may need:
2  
O  E 
2
E



 row total  column total 


E
grand total
df  r  1c  1
1. (10 points) Which Treatment Is Better? A randomized controlled trial was designed
to compare the effectiveness of splinting versus surgery in the treatment of carpal tunnel
syndrome. Results are given in the table below. The results are based on evaluations
made one year after the treatment. Using a 0.01 significance level, test the claim that
success is independent of the type of treatment. What do the results suggest about treating
carpal tunnel syndrome?
Splint Treatment
Surgery Treatment
Successful Treatment
60
67
Unsuccessful Treatment
23
6
Name:___________________
Date: 8/4/2011
STAT 50
Quiz 20
Some formulas you may need:
V .B.S.  ns X
F
2
V .B.S .
V .W .S .
n x 2   x 
2
df (numerator)  k  1
s 
df (deno min ator)  k (n  1)
2
nn  1
1. (10 points) In order to investigate the effectiveness of different diets, 40 people were
randomly selected who were on various diets for a year. The amount of weight the people
lost and what diets they were on is summarized in the table below. Use a 0.05
significance level to test the claim that a person’s average weight loss is the same for the
various diet plans listed in the table.
x
s2
Weight Watchers
Atkins
Jenny Craig
Nutrisystem
16
41
22
28
62
59
26
31
35
55
32
24
23
17
17
11
18
48
32
18
33
41
25
23
37
29
28
23
25
44
19
39
21
37
11
31
42
49
17
28
31.2
42
22.9
25.6
192.4
152
48.1
59.6