mini 4-2
docx
keyboard_arrow_up
School
University Of Connecticut *
*We aren’t endorsed by this school
Course
1000Q
Subject
Statistics
Date
Apr 3, 2024
Type
docx
Pages
4
Uploaded by MegaAnteaterMaster98
Assignment 4
Please follow the instructions in each exercise to run your simulations. Each graph must be
labeled with a title, axis labels, and a footnote with your name and section number. If the
assignment requires you to print the Session Window, click in the Session Window and type
your name and section number so you can identify your printout.
1. The Birthday Paradox: Suppose you are in a room with 24 other people. You would like
to answer the following question: What are the chances that at least two people in the room
have the same birthday?
a. Now that you know something about probability, take an “educated guess” at the
chances that at least two people in the room have the same birthday. If you think it is “very
unlikely” that at least two people have the same birthday, then assign a small probability to this
random event. If you think it is “very likely” that at least two people have the same birthday, then
assign a large probability to this random event. Write your answer here:
I think that it would be very unlikely that 2 people would share a birthday, I estimate to be
around 10%.
The probability of this random event is difficult to calculate mathematically; however, it is an
ideal simulation problem. Let’s simulate the problem and see how closely your “guess” agrees
with the simulated results.
To run the simulation, begin with the following information:
1. There are 365 days in a year. (We will ignore leap years). 2. There are 25 people in the room. (You and 24 others).
3. Each person could have any day of the year as his or her birthday, so each birthday is
equally likely.
Start your simulation with 1 room of 25 people:
Click on: CALC ® RANDOM DATA ® INTEGER
In the screen that appears, Generate
25 rows of data (representing the 25 people), Store in
column(s) C1 (representing 1 room), Minimum value is 1 (representing January 1), Maximum
value is 365 (representing December 31).
The question is: Are there at least two people with the same birthday?
In other words, are there at least two numbers in C1 that are the same? The easiest way to
answer this question is to summarize the data. Click on: STAT ® TABLES ® TALLY INDIVIDUAL VARIABLES
On the screen that appears, select C1 and click on COUNTS. Next click on OK, and in the
Session Window, you will see a summary table of C1. You will need to maximize the Session
Window to see the entire summary table. This table lists each of the different birthdays that
occurred in this simulation, as well as a count of the number of people who had that birthday.
Notice that most counts are 1’s. If you see a count of “2” or more anywhere in the COUNTS
column, then you have at least two people in the room with the same birthday.
b. Did you find at least one match in C1?
No, I did not
In order to calculate the probability of finding at least two people with the same birthday you
must repeat this experiment several times. You can generate several rooms with 25 people at the same time.
To do this, click on: CALC ® RANDOM DATA ® INTEGER
In the screen that appears, Generate
25 rows of data,
Store in columns C2-C50, Minimum
value is 1, Maximum value is 365.
You now have 49 more rooms with 25 people in each room. Now summarize each of the 50
columns so that you can look for matches (people with the same birthday). When you use
STAT ® TABLES ® TALLY Individual Variable command, you can select C1-C50, and the
summary tables for all 50 columns will appear in the Session Window. c. Maximize the Session Window. You will see the column tallies for all 50 columns. You
will look through the counts for each column to see whether you have a match in that column. A
match will be a ‘2’ or ‘3’ in the count column indicating that 2 or 3 people have that same
birthday. Start with the first five columns (C1 – C5), how many of these columns have at least
one match? Record this number in the table below next to C1-C5. Scroll through the Session
Window and repeat this process for the remaining columns.
Here are the results of one set of simulations for Col1 – Col5.
Tally
C1
C
o
C2
C
o
C3
C
o
C4
Count
C5
Count
u
nt
u
n
t
u
nt
31
1
29
1
6
1
4
1
20
1
54
1
38
1
7
1
12
1
52
1
57
1
43
1
14
1
19
1
67
1
79
1
51
1
52
1
28
1
77
1
85
1
53
1
53
1
38
1
112
1
95
1
56
1
84
1
39
1
119
1
105
1
69
1
86
1
48
1
121
1
121
1
112
1
104
1
56
1
131
1
123
1
123
1
105
1
62
1
149
1
125
1
150
1
109
1
67
1
161
1
139
1
166
1
120
1
102
1
173
1
140
2
173
1
137
1
127
1
193
1
173
1
179
1
145
1
129
1
195
1
217
1
186
1
151
1
156
1
216
1
219
1
188
1
160
1
181
1
223
1
248
1
193
1
215
1
190
1
241
1
250
1
227
1
220
1
221
1
272
1
251
1
236
1
268
1
236
1
281
1
254
1
251
1
272
1
267
1
291
1
266
1
258
1
288
1
269
1
294
1
299
1
269
1
292
1
270
1
303
1
302
1
325
1
316
1
273
1
309
1
317
1
327
1
334
1
280
1
313
1
340
1
335
1
350
1
319
1
314
1
N=
2
5
361
1
357
1
346
1
362
1
N=
2
5
N=
2
5
N=
25
N=
25
In this simulation, C1 had a match (2 people born on Day #140). Columns 2 through 5 did not
have any matches. So, for this simulation, you would enter ‘1’ in the space next to Col1-Col5
below.
Col1-Col5: __1__ Col 26-Col30: _3___
Col6-Col10: ___2_ Col31-Col35: __2__
Col11-Col15: _1___ Col36-Col40: __5__
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Col16-Col20: _5___ Col41-Col45: __5__
Col21-Col25: __5__ Col46-Col50: __7__
d. Of the 50 columns that you generated, how many of them had at least one matching
pair?
Out of the 50 columns, 33/50 have at least one pair
e. Based on your simulation, what is the probability
that, in a room with 25 people, at least
2 people have the same birthday? Note: the probability
is equal to (# of columns with a
matching pair / 50)
The probability is 0.66, or 66% f. How close is your experimental probability to the theoretical probability, which is .57?
The experimental probability is very close, 0.09 (9%) more than the theoretical probability. This is significantly more than my estimated probability, which was 10%.
Related Documents
Related Questions
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
A die is a cube with dots on each face. The faces have 1, 2, 3, 4, 5, or 6 dots. The table below is a computer simulation (from the software package Minitab) of the results of rolling a fair die 20 times.
DATA DISPLAY
ROW
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
1
3
2
4
5
4
5
3
5
3
4
2
5
2
2
2
5
3
2
3
1
4
(a) Assume that each number in the table corresponds to the number of dots on the upward face of the die. Is it appropriate that the same number appears more than once? Why?What is the outcome of the sixth roll?(b) If we simulate more rolls of the die, do you expect to get the same sequence of outcomes? Why or why not?
Step 1
(a) Assume that each number in the table corresponds to the number of dots on the upward face of the die. Is it…
arrow_forward
The stacked column graph below depicts the percentage of boys and girls in each room at the student union. Which of the following choices is true?
Question 9 options:
There are more girls than boys in the cafeteria and games room, but not in the lounge, lecture hall, and library.
There are more boys than girls in all of the rooms.
There are twice as many boys as girls at the Lounge.
There are more boys than girls in the cafeteria, games room, and the library, but not in the lounge and the lecture hall.
arrow_forward
Walter is a sales manager for a chain of car dealerships. He encourages the managers at each store to
spend as much time on the sales floor as they can. He is curious if this has any effect on the number of
cars sold. Each manager reports the number of hours per day he or she spends on the sales floor. From
this, Walter creates the scatterplot below showing sales and time on the floor. What information can
Walter infer from the scatterplot? Select all that apply.
10
9
8
1
1
3
4
7
Average Hours on Sales Floor
O There is a positive correlation between hours on the sales floor and sales.
O There is no correlation between hours on the sales floor and sales.
O There is a negative correlation between hours on the sales floor and sales.
O Walter should require all managers to spend more hours on the sales floor.
O Walter should make no changes to policies regarding hours on the sales floor for managers.
O Walter should help managers who spend little time on the sales floor find ways to spend…
arrow_forward
Please answer the following and show how to solve using the graphing calculator. Thank you
arrow_forward
The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy Conch, the owner, hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered the following sample information.
Customer
Amount of Tip
Amount of Bill
Number of Diners
Customer
Amount of Tip
Amount of Bill
Number of Diners
1
$
7.00
$
48.97
5
16
$
3.30
$
23.59
2
2
4.50
28.23
4
17
3.50
22.30
2
3
1.00
10.65
1
18
3.25
32.00
2
4
2.40
19.82
3
19
5.40
50.02
4
5
5.00
28.62
3
20
2.25
17.60
3
6
4.25
24.83
2
21
5.50
44.47
4
7
0.50
6.24
1
22
3.00
20.27
2…
arrow_forward
The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy Conch, the owner, hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered the following sample information.
Customer
Amount of Tip
Amount of Bill
Number of Diners
Customer
Amount of Tip
Amount of Bill
Number of Diners
1
$
6.05
$
73.22
1
16
$
3.30
$
23.59
2
2
4.50
28.23
4
17
3.50
22.30
2
3
1.00
10.65
1
18
3.25
32.00
2
4
2.40
19.82
3
19
5.40
50.02
4
5
5.00
28.62
3
20
2.25
17.60
3
6
4.25
24.83
2
21
1.40
41.80
5
7
.50
6.25
1
22
3.00
20.27
2…
arrow_forward
Make a “tree” diagram for a scenario: You and two friends go to dairy queen. You are selecting from chocolate and vanilla.
arrow_forward
You are using cash to pay a $20 parking ticket. In your wallet you have one $5-dollar bill, three
$10-dollar bills, and two $20 dollar bills, and you draw out one bill at a time at random until you
have at least $20. If you keep track of each bill as you draw it out of the wallet, how many different
ways are there for you to get at least $20?
arrow_forward
Please answer the question in the photo. Thank you!
arrow_forward
Andrea conducted a survey in which she collected data on the percentage of people who like horror films and the percentage of people who like romantic dramas. Which of the following could sufficiently display the data if only the two given categories are to be included?
Pie Chart
Bar Graph
Neither pie chart or bar graph
Either a pie chart or bar graph
arrow_forward
Experimental or Observational: A group of students is interested in knowing if the number of times they can sink a basketball is related to the color of the basketball. The students shoot a series of baskets and record their success using a regulation colored basketball. They then switch to a blue colored basketball and shoot the same series of baskets.
.
arrow_forward
please do the last question(Q3) as well
Define a game as follow: you begin with an urn that contains a mixture of black and white balls, and during the game you have access to as many extra black and white balls as you need.
In each move of the game, you remove two balls from the urn without being able to see what colour they are. Then you look at their colour and do the following:
If the balls are the same colour, you keep them out of the urn and put a black ball in the urn.
if the balls are different colours, you keep the black one out of the urn and put the white one back into the urn.
Each move reduces the number of balls by one, and the game will end when only one ball is left in the urn.
In this you will figure out how to predict the colour of the last ball in the urn and prove your answer using mathematical induction.
Q1) Draw diagrams to map out all the possibilities for playing the game starting with two balls in the urn, then three balls, then four balls. For each case…
arrow_forward
If there is an interaction between the variables of “activity level” and “time of day,” this means that activity level does not have the same effect at different times of day.
Group of answer choices
True
False
arrow_forward
Continue monitoring the process. A second ten days of data have been collected, see table labeled “2nd 10 Days of Monitoring Reservation Processing Time” in the Data File.
Develop Xbar and R charts for the 2nd 10 days of monitoring. Plot the data for the 2nd 10 days on the Xbar and R charts.
Is the reservation process for the 2nd 10 days of monitoring in control? If the control chart indicates an out-of-control process, note which days, the pattern, and whether it is the Xbar or R chart.
Based on the X-bar and R Charts that you developed for the 2nd 10 days of data, is the process in control?
Group of answer choices
No. The X-bar and R Charts are both out of control.
No. The X-bar Chart is in control, but the R Chart is out of control.
No. The R Chart is in control, but the X-bar Chart is out of control.
Yes. The X-bar and R Charts are both in control.
arrow_forward
dlo
Air Pollution The Environmental Protection Agency must investigate 10 mills for complaints of air pollution. How many different
ways can a representative select 5 of these to investigate this week? Use a graphing calculator.
The number of different ways for a representative to select 5 out of 10 mills to investigate is
arrow_forward
In class, we compared healing times for females who received an experimental cold sore medicine. The data for the male control and treatment groups are provided below; they represent the number of days that passed before the sores were completely gone. In your notebook, make a dotplot for each group.
Control: 20,13,22,21,16,5,21,11,16,14,15,15,13,16,10,17,16,11,21
Treatment: 11,16,8,16,15,12,11,12,12,9,11,19,16,13,5,15,12,8,11
Part A: Calculate the mean healing time for the control group, rounding your result to the nearest hundredth. In your notebook, mark an "X" on the horizontal axis of your dotplot to show the mean.Mean = daysPart B: Calculate the mean healing time for the treatment group, rounding your result to the nearest hundredth. In your notebook, mark an "X" on the horizontal axis of your dotplot to show the mean.Mean = days
arrow_forward
s
arrow_forward
CONTEXT:Paul the Octopus correctly predicted the winner of 8 out of 8 games played in the 2010 World Cup. His success brought him lots of fame, including being covered by various news outlets writing about Paul’s “psychic” abilities.
In Germany, soccer fans loved watching as Paul the Octopus was presented with two boxes in his tank, each containing a mussel and decorated with the country’s flag of a soccer team. Whichever box Paul chose to eat his mussel from was considered his “prediction” for the winner of the soccer game.
Key question to investigate: Could Paul’s success rate have happened by chance? In other words, is Paul’s success rate of 8 out of 8 unusual enough that a model based on random chance is reasonable, or should this model be rejected in favor of a different model to explain his prediction of successes?
Our null model (or hypothesis) is that the probability of choosing either box is 0.5.
The alternative model (or hypothesis) is that the probability is something…
arrow_forward
I want you to collect data and use it to make a statistical graph (pie, bar, line, or histogram).
You can collect your data or you can use an already existing data set. If you elect to collect your own data, you must clearly detail how the data was collected in your post. If you used an already existing data set, you must cite your source for credit. The graph you construct CANNOT be done by hand for credit.The graph you construct MUST be your own work. If you copy an existing graph or mimic an existing one exactly, you will not receive credit.Your post must contain how the data was collected (or a citation leading us to your data set) AND a picture of the graph you create.
arrow_forward
Please fill in the blanks and select the correct answers over the image provided. Thank you
arrow_forward
The similarities and differences between three concepts science, non-science and pseudoscience.
Using venn diagram.
arrow_forward
A city official would like to know if there is public support for increasing funding for arts programs. To collect data, the
city official stands outside a concert hall after a show and surveys every 25th person to exit and asks their opinion
about raising funds for the arts. Which of the following describes the population in this scenario?
all residents of the city
the members of the city council
all city residents who support the arts
the people surveyed by the city official
arrow_forward
SEE MORE QUESTIONS
Recommended textbooks for you

Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL

Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill

Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Related Questions
- This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A die is a cube with dots on each face. The faces have 1, 2, 3, 4, 5, or 6 dots. The table below is a computer simulation (from the software package Minitab) of the results of rolling a fair die 20 times. DATA DISPLAY ROW C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 1 3 2 4 5 4 5 3 5 3 4 2 5 2 2 2 5 3 2 3 1 4 (a) Assume that each number in the table corresponds to the number of dots on the upward face of the die. Is it appropriate that the same number appears more than once? Why?What is the outcome of the sixth roll?(b) If we simulate more rolls of the die, do you expect to get the same sequence of outcomes? Why or why not? Step 1 (a) Assume that each number in the table corresponds to the number of dots on the upward face of the die. Is it…arrow_forwardThe stacked column graph below depicts the percentage of boys and girls in each room at the student union. Which of the following choices is true? Question 9 options: There are more girls than boys in the cafeteria and games room, but not in the lounge, lecture hall, and library. There are more boys than girls in all of the rooms. There are twice as many boys as girls at the Lounge. There are more boys than girls in the cafeteria, games room, and the library, but not in the lounge and the lecture hall.arrow_forwardWalter is a sales manager for a chain of car dealerships. He encourages the managers at each store to spend as much time on the sales floor as they can. He is curious if this has any effect on the number of cars sold. Each manager reports the number of hours per day he or she spends on the sales floor. From this, Walter creates the scatterplot below showing sales and time on the floor. What information can Walter infer from the scatterplot? Select all that apply. 10 9 8 1 1 3 4 7 Average Hours on Sales Floor O There is a positive correlation between hours on the sales floor and sales. O There is no correlation between hours on the sales floor and sales. O There is a negative correlation between hours on the sales floor and sales. O Walter should require all managers to spend more hours on the sales floor. O Walter should make no changes to policies regarding hours on the sales floor for managers. O Walter should help managers who spend little time on the sales floor find ways to spend…arrow_forward
- Please answer the following and show how to solve using the graphing calculator. Thank youarrow_forwardThe Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy Conch, the owner, hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered the following sample information. Customer Amount of Tip Amount of Bill Number of Diners Customer Amount of Tip Amount of Bill Number of Diners 1 $ 7.00 $ 48.97 5 16 $ 3.30 $ 23.59 2 2 4.50 28.23 4 17 3.50 22.30 2 3 1.00 10.65 1 18 3.25 32.00 2 4 2.40 19.82 3 19 5.40 50.02 4 5 5.00 28.62 3 20 2.25 17.60 3 6 4.25 24.83 2 21 5.50 44.47 4 7 0.50 6.24 1 22 3.00 20.27 2…arrow_forwardThe Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy Conch, the owner, hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered the following sample information. Customer Amount of Tip Amount of Bill Number of Diners Customer Amount of Tip Amount of Bill Number of Diners 1 $ 6.05 $ 73.22 1 16 $ 3.30 $ 23.59 2 2 4.50 28.23 4 17 3.50 22.30 2 3 1.00 10.65 1 18 3.25 32.00 2 4 2.40 19.82 3 19 5.40 50.02 4 5 5.00 28.62 3 20 2.25 17.60 3 6 4.25 24.83 2 21 1.40 41.80 5 7 .50 6.25 1 22 3.00 20.27 2…arrow_forward
- Make a “tree” diagram for a scenario: You and two friends go to dairy queen. You are selecting from chocolate and vanilla.arrow_forwardYou are using cash to pay a $20 parking ticket. In your wallet you have one $5-dollar bill, three $10-dollar bills, and two $20 dollar bills, and you draw out one bill at a time at random until you have at least $20. If you keep track of each bill as you draw it out of the wallet, how many different ways are there for you to get at least $20?arrow_forwardPlease answer the question in the photo. Thank you!arrow_forward
- Andrea conducted a survey in which she collected data on the percentage of people who like horror films and the percentage of people who like romantic dramas. Which of the following could sufficiently display the data if only the two given categories are to be included? Pie Chart Bar Graph Neither pie chart or bar graph Either a pie chart or bar grapharrow_forwardExperimental or Observational: A group of students is interested in knowing if the number of times they can sink a basketball is related to the color of the basketball. The students shoot a series of baskets and record their success using a regulation colored basketball. They then switch to a blue colored basketball and shoot the same series of baskets. .arrow_forwardplease do the last question(Q3) as well Define a game as follow: you begin with an urn that contains a mixture of black and white balls, and during the game you have access to as many extra black and white balls as you need. In each move of the game, you remove two balls from the urn without being able to see what colour they are. Then you look at their colour and do the following: If the balls are the same colour, you keep them out of the urn and put a black ball in the urn. if the balls are different colours, you keep the black one out of the urn and put the white one back into the urn. Each move reduces the number of balls by one, and the game will end when only one ball is left in the urn. In this you will figure out how to predict the colour of the last ball in the urn and prove your answer using mathematical induction. Q1) Draw diagrams to map out all the possibilities for playing the game starting with two balls in the urn, then three balls, then four balls. For each case…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell

Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL

Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill

Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell