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Peck/Short/Olsen-Intro to Stats & Data Analysis 6e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 15 / 109

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving...  ()

Question
Points
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15/109 (13.8%)
  • Instructions

    Introduction to Statistics and Data Analysis, 6th Edition, by Peck, Short, and Olsen, published by Cengage Learning, lowers the reading level from the previous edition and significantly increases homework scaffolding for difficulty level. In order to get students thinking statistically, this text stresses interpretation and communication of statistical information through hands-on, activity based learning using real data. Written in compliance with the GAISE college report and employing techniques based on modern research into student learning, this text places emphasis on how concepts apply to students and the world around them, then gets into methods using data analysis tools or hand-calculations where necessary. The 6th edition contains new sections on randomization-based inference: bootstrap methods for simulation-based confidence intervals and randomization tests of hypotheses. The WebAssign component for this text engages students with an interactive eBook and several other resources.

    New for Spring 2021! Question 1 is an example of a Concept Video Question. (CV) Concept Video questions provide students with a Concept Video along with two to three comprehension questions. Concept Videos are 7-10 minutes in length and are designed to help students with big picture understanding of statistics.

    New for Spring 2021! Question 2 is an example of a new Select Your Scenario question type. (SYS) Select Your Scenario problems provide students with 3 different contexts to choose from. They select the scenario most relevant to them, and then solve the problem. Regardless of which scenario the student chooses, they will be required to answer questions demonstrating knowledge of a learning objective, making them the perfect questions to assign toward the end of a chapter. Students can use SALT to answer this question.

    Question 3 shows multiple choice questions to categorize variable types.

    Question 4 asks students to enter the test statistic and P-value then answer multiple choice questions about the conclusion. Students can use SALT to answer this question.

    Question 5 asks students to numerically enter the regression line and some predicted values.

    Question 6 is an example of a Statistical Lab. These activities support SPSS, Minitab, R, JMP, Excel, and TI 83/84 or TI-Inspire calculators.

    Question 7 and 8 ask students to numerically enter statistics then answer multiple choice questions. Students can use SALT to answer these questions.

    Question 9 is a Simulation Question utilizing the JMP Applet.

    Question 10 is a Concept Question where students are asked to provide a short answer to a prompt, then answer a multiple choice question about the sample prompt, then reflect on their original answer.

    Question 11 walks the student through creation of a simple sampling distribution and graph.

    Question 12 has students create a confidence interval at two levels and compare widths. Students can use SALT to answer this question.

    Question 13 is a Stats in Practice question that demonstrates the use of videos displayed within a question, followed by multiple choice and discussion questions in a unique two-part accordion style of display.

    Question 14 highlights Milestone 1, the first step in presenting and tracking Project Milestones for a statistical research project. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

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Watch the video below then answer the questions that follow.
  1. What is the first step in the statistical research process?
         Correct: Your answer is correct.
  2. It is important to have very strong math skills in order to be successful in a statistics course.
         Correct: Your answer is correct.
  3. Statistics is used in which of the following industries?
         Correct: Your answer is correct.
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Select Your Scenario:
This problem contains data for 3 different scenarios: Travel and Tourism, Business, and Sports.
Read the scenarios, and once finished, you will be asked to select which scenario you would like to be assessed on.
You will not be asked to answer questions for the other 2 scenarios.
When you travel by airplane, have you ever wondered about whether your flight might be delayed from taking off or from landing? This is an important consideration as you will need to arrange transportation to your final destination after you arrive at the airport. To help track airline performance, the U.S. Bureau of Transportation Statistics of the Department of Transportation publishes statistics. For the purposes of this dataset, a flight is considered delayed if it arrived at (or departed from) the gate 15 minutes or more after the scheduled arrival (or departure) time as reflected in the Computerized Reservation System.
We will explore the distribution of monthly percentage of domestic flights delayed in the United States using a sample of data for the years 2010 through 2019 by making a histogram with bins starting at 9% and a bin width of 3%. We will then determine the z-scores for a delayed percentage of (a) 16% and (b) 27%.
The dataset consists of the percentage of flights delayed for each month for years 2010 through 2019 for domestic flights in the United States.
Airline Performance: Bureau of Transportation Statistics. (2020, September 1). On-Time Performance - Flight Delays at a Glance. United States Department of Transportation. https://www.transtats.bts.gov/HomeDrillChart.asp
Year Month Delayed (%)
2010 January 18.58
2010 February 19.66
2010 March 18.3
2010 April 13.83
2010 May 18.55
Undergraduate business students at a public university in the midwestern United States ran a café one semester and collected data each business day to help make sound business decisions and to be more profitable. Among other things, the daily total cash register sales were recorded.
We will explore the distribution of daily total sales for this café using a sample of data from one semester by making a histogram of Sales ($) with bins starting at $60 and a bin width of $25. We will then determine the z-scores for a day when total sales were (a) $210 and (b) $110.
The dataset consists of data recorded across one semester including an index number that puts the observations in chronological order, the day of the week, and the total sales in dollars.
http://jse.amstat.org/jse_data_archive.htm
Index Day of Week Sales($)
1 Tuesday 199.95
2 Wednesday 195.74
3 Thursday 102.68
4 Friday 162.88
5 Monday 101.76
It goes without saying that professional basketball players are tall. Height obviously matters when it comes to playing basketball and tall people are more efficient because they can reach the basket easily, allowing for more points per game, as well as more rebounds and blocked shots. If you watch National Basketball Association (NBA) games regularly, you certainly notice that many players are quite tall.
We will explore the distribution of NBA player heights using a sample of players active in the 2019-2020 season by making a histogram of "HEIGHT (INCHES)" with bins stating at 68 inches and a bin width of 2 inches. We will then determine the z-scores for players who are (a) 71 inches (5'11") and (b) 83 inches (6'11").
The dataset consists of the NBA player's name, team, and height, measured in inches, for players active in the 2019-2020 season.
https://www.nba.com/stats/players/bio/
Player Team Height (Inches)
Aaron Gordon ORL 80
Aaron Holiday IND 73
Abdel Nader OKC 77
Adam Mokoka CHI 77
Admiral Schofield WAS 77
Click the link below to begin the question by choosing a topic.
Pick your topic.
Choose the topic on which you would like to be assessed. Once you select your scenario, you cannot change your topic.
     Correct: Your answer is correct.
Note: If you select Skip, you will be assessed on the Travel and Tourism topic.
Question
Select Your Scenario:
First, select the tab that corresponds to the topic you chose above.
Note: Click the SALT button in the tab corresponding to the topic you chose.
When you travel by airplane, have you ever wondered about whether your flight might be delayed from taking off or from landing? This is an important consideration as you will need to arrange transportation to your final destination after you arrive at the airport. To help track airline performance, the U.S. Bureau of Transportation Statistics of the Department of Transportation publishes statistics. For the purposes of this dataset, a flight is considered delayed if it arrived at (or departed from) the gate 15 minutes or more after the scheduled arrival (or departure) time as reflected in the Computerized Reservation System.
We will explore the distribution of monthly percentage of domestic flights delayed in the United States using a sample of data for the years 2010 through 2019 by making a histogram with bins starting at 9% and a bin width of 3%. We will then determine the z-scores for a delayed percentage of (a) 16% and (b) 27%.
The dataset consists of the percentage of flights delayed for each month for years 2010 through 2019 for domestic flights in the United States.
Airline Performance: Bureau of Transportation Statistics. (2020, September 1). On-Time Performance - Flight Delays at a Glance. United States Department of Transportation. https://www.transtats.bts.gov/HomeDrillChart.asp
Year Month Delayed (%)
2010 January 18.58
2010 February 19.66
2010 March 18.3
2010 April 13.83
2010 May 18.55
Import the dataset into SALT for analyzing.
A button hyperlink to the SALT program that reads: Use SALT.
Undergraduate business students at a public university in the midwestern United States ran a café one semester and collected data each business day to help make sound business decisions and to be more profitable. Among other things, the daily total cash register sales were recorded.
We will explore the distribution of daily total sales for this café using a sample of data from one semester by making a histogram of Sales ($) with bins starting at $60 and a bin width of $25. We will then determine the z-scores for a day when total sales were (a) $210 and (b) $110.
The dataset consists of data recorded across one semester including an index number that puts the observations in chronological order, the day of the week, and the total sales in dollars.
http://jse.amstat.org/jse_data_archive.htm
Index Day of Week Sales($)
1 Tuesday 199.95
2 Wednesday 195.74
3 Thursday 102.68
4 Friday 162.88
5 Monday 101.76
Import the dataset into SALT for analyzing.
A button hyperlink to the SALT program that reads: Use SALT.
It goes without saying that professional basketball players are tall. Height obviously matters when it comes to playing basketball and tall people are more efficient because they can reach the basket easily, allowing for more points per game, as well as more rebounds and blocked shots. If you watch National Basketball Association (NBA) games regularly, you certainly notice that many players are quite tall.
We will explore the distribution of NBA player heights using a sample of players active in the 2019-2020 season by making a histogram of "HEIGHT (INCHES)" with bins stating at 68 inches and a bin width of 2 inches. We will then determine the z-scores for players who are 71 inches (5'11") and (b) 83 inches (6'11").
The dataset consists of the NBA player's name, team, and height, measured in inches, for players active in the 2019-2020 season.
https://www.nba.com/stats/players/bio/
Player Team Height (Inches)
Aaron Gordon ORL 80
Aaron Holiday IND 73
Abdel Nader OKC 77
Adam Mokoka CHI 77
Admiral Schofield WAS 77
Import the dataset into SALT for analyzing.
A button hyperlink to the SALT program that reads: Use SALT.
After you have clicked the tab for your selected topic and read the problem, answer the questions below.
(a)
Use SALT to summarize the data and fill in the following table, rounding values to four decimal places as needed.
Variable N Mean Standard Deviation Median Minimum Value Maximum Value
Numerical Variable Incorrect: Your answer is incorrect. Incorrect: Your answer is incorrect.
(b)
Create a histogram with "Starting Point" and "Bin/Class Width" values asked for.
The distribution for this variable Incorrect: Your answer is incorrect. mound shaped and at least roughly symmetric.
(c)
Determine the relative standing for the two data values of interest using the z-score formula appropriate for samples. Round your answers to two decimal places.
Data value (a).
z = 
x x
s
 
 =  Incorrect: Your answer is incorrect.
Data value (b).
z = 
x x
s
 
 =  Incorrect: Your answer is incorrect.
Data value (a) is standard deviations Incorrect: Your answer is incorrect. the mean whereas data value (b) is standard deviations the mean. (Remember to take the absolute value of the z-score to determine the number of standard deviations each data value is away from the mean.)
(d)
Most data points are within three standard deviations of the mean. In other words, most observations will have a z-score that is larger than 3 and less than 3.
Find the data value with a z-score of 3, rounded to two decimal places.
x = z · s + x
 =  Incorrect: Your answer is incorrect.
Find the data value with a z-score of 3, rounded to two decimal places.
x = z · s + x
 =  Incorrect: Your answer is incorrect.
Our sample's minimum value Incorrect: Your answer is incorrect. further than 3 standard deviations below the mean. Our sample's maximum Correct: Your answer is correct. further than 3 standard deviations above the mean. Upon further inspection of the histogram in SALT it can be observed that Incorrect: Your answer is incorrect. observations would have a z-score between 3 and 3.


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Classify each of the following attributes as either categorical or numerical. For those that are numerical, determine whether they are discrete or continuous.
(a) Number of students in a class of 35 who turn in a term paper before the due date.
     Correct: Your answer is correct.


(b) Gender of the next baby born at a particular hospital.
     Correct: Your answer is correct.


(c) Amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda pop.
     Correct: Your answer is correct.


(d) Thickness of the gelatin coating of a vitamin E capsule.
     Correct: Your answer is correct.


(e) Birth order classification (only child, firstborn, middle child, lastborn) of a math major.
     Correct: Your answer is correct.

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In a survey of 1,000 women aged 22 to 35 who work full time, 555 indicated that they would be willing to give up some personal time in order to make more money. The sample was selected in a way that was designed to produce a sample that was representative of women in the targeted age group.
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Do the sample data provide convincing evidence that the majority of women aged 22 to 35 who work full-time would be willing to give up some personal time for more money? Test the relevant hypotheses using
α = 0.01.
Find the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z = 
P-value = 
State your conclusion.
    
(b)
Would it be reasonable to generalize the conclusion from part (a) to all working women? Explain why or why not.
    

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Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values.
β = slope of population regression line = 0.019
α = y intercept of population regression line
= 5
(a) What is the equation of the population regression line?
y =


(b) What is the mean value of gas usage for houses with 2200 sq. ft. of space?


(c) What is the average change in usage associated with a 1 sq. ft. increase in size?


(d) What is the average change in usage associated with a 100 sq. ft. increase in size?


You may need to use the appropriate table in Appendix A to answer this question.
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Statistical Lab

  • Background

    The National Institutes of Health conducts ongoing surveys of US adults called the Health Information National Trends Survey (hereafter abbreviated HINTS).
    From the National Institutes of Health: "The HINTS data collection program was created to monitor changes in the rapidly evolving field of health communication. Survey researchers are using the data to understand how adults 18 years and older use different communication channels, including the Internet, to obtain vital health information for themselves and their loved ones...."
    A doctor and a patient are talking in an examination room.
    The most recent round of data collection occurred over the course of September 2013November, 2013 in HINTS 4 Cycle 3. In this lab, you will be using a subset of the HINTS 4 Cycle 3 data to practice creating effective and informative graphical representations of data, which may include histograms and pie charts.
  • About the Data

    For this lab, you need to download the hintsdata.csv dataset. The variables you will be working with are as follows.
    • Ageassume each person's age was rounded to the nearest year; for example, a person in the age
      range [19.5, 20.5)
      would have a reported age of 20, and a person in the
      range [20.5, 21.5)
      would have a reported age of 21, and so on.
    • Genderthe gender of the respondent; categories include 1 = Male and 2 = Female.
    • GeneralHealthhow the respondent rates their overall health; categories include 1 = Excellent, 2 = Very Good, 3 = Good, 4 = Fair, 5 = Poor.
  • General Notes

    A few important aspects of creating effective graphical displays of data include the following.
    1. labeling your graphs with descriptive titles
    2. ensuring that the x- and y-axes have appropriate labels
    3. setting the axes to meaningful and/or useful scales
    Your graphs are expected to have these three characteristics.
  • Tech Guide

    You will need to use the Excel Tech Guide.
  • Lab Questions

    Create a histogram of the variable Age with class intervals 10 years wide. (Submit a file with a maximum size of 1 MB.)

    This answer has not been graded yet.

    Describe the shape of the above histogram.
    The distribution is Incorrect: Your answer is incorrect. , centered near Incorrect: Your answer is incorrect. , with Correct: Your answer is correct. variability.
    Create a pie chart of the variable GeneralHealth. (Submit a file with a maximum size of 1 MB.)

    This answer has not been graded yet.

    Describe how the majority of people in the survey feel about their general state of health.
    The majority of people in the survey feel that their general state of health is .
    You wish to determine if the age of the respondents who perceive themselves to be in good health differs from the age of the respondents who perceive themselves to be in poor health. Do this by creating two histograms. For the first histogram, plot the variable Age using only the data from respondents who rate their overall health as Excellent, Very Good, or Good. For the second histogram, plot the variable Age using only the data from respondents who rate their overall health as Fair or Poor. Make sure to label your histograms and make sure that they have the same limits for the x-axis, y-axis, and class intervals, so that they can be directly compared. (Submit a file with a maximum size of 1 MB.)

    This answer has not been graded yet.

    Briefly discuss.

    This answer has not been graded yet.

    Compare how men and women rate their general state of health using a comparative chart. Using your chart, briefly compare and contrast how men and women rate their general state of health.

    This answer has not been graded yet.

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  • This exercise will build problem-solving skills.
  • Master It (.MI) questions include stepped-out tutorials to help students learn the concept.

The following data are costs (in cents) per ounce for nine different brands of sliced Swiss cheese.
27    64    36    44    70    84    47    54    49
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Calculate the variance for this data set. (Round your answer to four decimal places.)
Calculate the standard deviation for this data set. (Round your answer to four decimal places.)
Correct: Your answer is correct.
(b)
If a very expensive cheese with a cost per slice of 150 cents was added to the data set, how would the values of the mean and standard deviation change?
The addition of the very expensive cheese would Correct: Your answer is correct. the value of the mean and Correct: Your answer is correct. the value of the standard deviation.

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  • This exercise will explore real data with technology.
  • The Statistical Analysis and Learning Tool (SALT) is designed by statisticians, for statisticians, to help you get introductory students deeply engaged in data manipulation, analysis, and interpretation without getting bogged down in complex computations.

Fiber content (in grams per serving) for 18 high fiber cereals are shown below.
Fiber Content
5 11 11 5 9 5 12 12 9
13 11 9 12 5 14 5 9 9
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Find the median, quartiles, and interquartile range for the fiber content data set.
median = Correct: Your answer is correct. lower quartile = upper quartile = interquartile range =
(b)
Explain why the minimum value for the fiber content data set and the lower quartile for the fiber content data set are equal.
    

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The population (in thousands) of 52 cities was collected and the graph and summary statistics of this data are given in the JMP Applet.
  • Cities' populations

    CITY POP
    ALBANY 846
    ALBUQUERQUE 486
    ATLANTA 2657
    ATLANTIC CITY 303
    BALTIMORE 2303
    BOSTON 2842
    BURLINGTON 127
    CHARLESTON 502
    CHARLOTTE 1091
    CHEYENNE 76
    CHICAGO 6199
    CINCINNATI 1438
    CLEVELAND 1851
    CITY POP
    DENVER 1645
    DES MOINES 385
    DETROIT 4362
    DUBUQUE 91
    GALVESTON-T.C. 211
    HARRISBURG 584
    HARTFORD 748
    HOUSTON 3228
    HUNTINGTON 323
    INDIANAPOLIS 1229
    JACKSON 396
    JACKSONVILLE 878
    LOS ANGELES 8505
    CITY POP
    LOUISVILLE 967
    MADISON 347
    MIAMI 1791
    MILWAUKEE 1389
    MINNEAPOLIS 2336
    MOBILE 438
    MONTGOMERY 297
    NASHVILLE 956
    NEW ORLEANS 1321
    NEW YORK 8529
    NORFOLK 1346
    OKLAHOMA CITY 975
    OMAHA 616
    CITY POP
    PHILADELPHIA 4866
    PHOENIX 1960
    PORTLAND 210
    PORTLAND 1168
    RALEIGH 665
    SALT LAKE CITY 1055
    SAN FRANCISCO 1590
    SEATTLE 1796
    SPOKANE 355
    ST. LOUIS 2458
    WASHINGTON 3646
    WICHITA 475
    WILMINGTON 559
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Concept Question
This question is related to sampling distribution.
Part 1 of 3
If a normal population has a standard deviation σ = 31.6, what is the standard error of the mean (standard deviation of the x's) if samples of size 16 are selected? What is the standard error if samples of size 49 are taken? What is the standard error if samples of size 100 are taken? (Round your answers to two decimal places.)
Regardless of sample size, why is the standard deviation of the x's always smaller than the standard deviation of the population?

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Consider the following population: {5, 6, 7, 8}. For this population the mean is
μ
5 + 6 + 7 + 8
4
 = 6.5
Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account).
5, 6 5, 7 5, 8 6, 5 6, 7 6, 8
7, 5 7, 6 7, 8 8, 5 8, 6 8, 7
(a)
Calculate the sample mean for each of the 12 possible samples.
Sample Sample Mean
5, 6
5, 7
5, 8
6, 5
6, 7
6, 8
7, 5
7, 6
7, 8
8, 5
8, 6
8, 7
(b)
Use the sample means to construct the sampling distribution of x. Display the sampling distribution as a density histogram.

(c)
Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of part (a), construct the sampling distribution of x. (Hint: There are 16 different possible samples in this case.)

(d)
In what ways are the two sampling distributions of parts (b) and (c) similar? In what ways are they different? (Select all that apply.)

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A certain article indicates that in a sample of 1,000 dog owners, 640 said that they take more pictures of their dog than their significant others or friends. In addition, 420 said that they are more likely to complain to their dog than to a friend. Suppose that it is reasonable to consider this sample as representative of the population of dog owners.
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Construct a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends. (Round your answers to three decimal places.)
,
Interpret the interval.
    
(b)
Construct a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend. (Round your answers to three decimal places.)
,
Interpret the interval.
    
(c)
Give two reasons why the confidence interval in part (b) is wider than the interval in part (a).
First, the confidence level in part (b) is the confidence level in part (a), so the z critical value for part (b) is the z critical value for part (a). Second, the in part (b) is that in part (a).

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Stats in Practice

  • Part I - Multiple Choice Questions

    The video opens with: "Fewer young people are putting on sunscreen when they are having fun in the sun." They support this conclusion by citing the results of a Center for Disease (CDC) study, in which researchers estimated what value in both 2001 and 2011?
        
    In this CDC study, why is it correct to say that researchers "estimated" a particular population characteristic rather than say the researchers "calculated" that value?
        
    The video discusses a study conducted by University of Michigan researchers who found that "close community ties can reduce heart attack risk for those over 50." In this study, researchers probably collected a sample of individuals, and for each, measured numerical variables (such as age or weight) as well as categorical variables (such as gender or whether a person has had a heart attack). Which of the following is also a numerical variable that researchers may have measured in this study?
        
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/18
 

Milestone 1: Research Design

  • Question 1

    What is your research question?
    Your research question should be based on a topic that interests you and that you can reasonably obtain data for. Try to make your research question as specific as possible. Form a research question about a population that you will be able to sample. Some examples of research questions are: "Are students at my college able to taste the difference between regular coffee and decaffeinated coffee?", "Does the GPA, age, and number of credits needed for graduation for juniors at my university differ between transfer students and non-transfer students?", "Have the new water rates in my water district changed residents' water usage habits?", and "Do recent graduates from the business department at my university get larger starting salaries on average if they have participated in a summer internship?"

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