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Utts and Heckard - Mind on Statistics 5/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 1 / 149

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

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  • Instructions

    Mind on Statistics Fifth Edition, written by Utts and Heckard and published by Cengage Learning, helps students develop a conceptual understanding of statistical ideas by showing them how to find meaning in data. This textbook engages students' curiosity with intriguing questions, and explains statistical topics in the context of interesting, useful examples, and case studies. The WebAssign component for this text engages students with an interactive eBook, Active Examples with worked-out solutions, and a variety of textbook resources including lecture videos and PowerPoint lectures slides.

    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 is an Active Example that guides students through the process needed to master a concept using actual textbook examples. Students can use SALT to answer this question.

    Question 4 displays a data set with regression equation for the data and asks students to interpret and use the equation to make predictions.

    Question 5 requires students to create a contingency table, then calculate percents of given outcomes to determine relationships between symptoms.

    Question 6 has the student complete two-way tables and then verify the calculation of the chi-square statistic.

    Question 8 asks the student to calculate different probabilities using deMorgan's law and interpret those results.

    Question 9 requires the student to calculate probabilities using a tree diagram.

    Questions 11 and 12 provide links to SALT that students may use to calculate probabilities.

    Question 13 provides a link to SALT that students may use to calculate confidence intervals.

    Question 14 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 type of display.

    Question 15 is a Test Bank question that highlights the ability to grade short answer style questions automatically using multiple choice.

    Question 16 is a Simulation Question utilizing the JMP Applet.

    Question 17 is an example of a Statistical Lab.

    Question 18 highlights Milestone 1, the first step in presenting and tracking Project Milestones for a statistical research project.

    View the complete list of WebAssign questions available for this textbook. 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.

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

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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?
        
  2. It is important to have very strong math skills in order to be successful in a statistics course.
        
  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) 14% 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) $200 and (b) $100.
The dataset consists of data recorded across one semester including an index number that puts the observations in chronological order, the day of the week, and the total sales in dollars.
http://jse.amstat.org/jse_data_archive.htm
Index Day of Week Sales($)
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) 72 inches (6'0") and (b) 85 inches (7'1").
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.

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Example 2.16
Here are weights (in pounds) of 18 men who were on the crew teams at Oxford and Cambridge universities.
University Weight
Cambridge 191.5
Cambridge 186
Cambridge 197.5
Cambridge 188
Cambridge 217
Cambridge 206.5
Cambridge 189
Cambridge 181.5
Cambridge 112
Oxford 189
Oxford 187.5
Oxford 207
Oxford 187.5
Oxford 198.5
Oxford 205.5
Oxford 177
Oxford 186
Oxford 112.5
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Read over the list. Do you notice anything unusual? The last weight given in each list is very different from the others. In fact, those two men were the coxswains for their teams (the light-weights who give the orders), while the other men were the rowers. What is the mean weight for the crew team members? (Round your answers to four decimal places.)
(a) If all members are included, it is lb.

(b) If only the rowers are included, it is lb.

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Dataset temperature is available here.
The average August temperatures (y) and geographic latitudes (x) of 20 cities in the United States are given in the following table.
City Latitude Aug Temp
Miami FL 26 83
Houston TX 30 82
Mobile AL 31 82
Phoenix AZ 33 92
Dallas TX 33 85
Los Angeles CA 34 75
Memphis TN 35 81
Norfolk VA 37 77
San Francisco CA 38 64
Baltimore MD 39 76
Kansas City MO 39 76
Washington DC 39 74
Pittsburgh PA 40 71
Cleveland OH 41 70
New York NY 41 76
Boston MA 42 72
Syracuse NY 43 68
Minneapolis MN 45 71
Portland OR 46 69
Duluth MN 47 64
The regression equation for these data is expressed with the following formula.
 y^^\^ = 113.6 - 1.01 x
(a) What is the slope of the line? Interpret the slope in terms of how mean August temperature is affected by a change in latitude.
    

(b) Estimate the mean August temperature for a city with latitude of 36. (Round your answer to two decimal places.)
°F

(c) San Francisco CA has a mean August temperature of 64, and its latitude is 38. Use the regression equation to estimate the mean August temperature in San Francisco CA, and then calculate the prediction error (residual) for San Francisco CA. (Round the answer to two decimal places.)
°F

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Do grumpy old men have a greater risk of having coronary heart disease than men who aren't so grumpy? Researchers examined this question in a prospective observational study. For seven years, the researchers studied men between the ages of 46 and 90 years old. All study participants completed a survey of anger symptoms at the beginning of the study period. Among 210 men who had no anger symptoms, there were 4 cases of coronary heart disease. Among 557 men who had the most anger symptoms, there were 50 cases of coronary heart disease.
(a) Construct a contingency table for the relationship between degree of anger and the incidence of heart disease.

Heart disease No heart disease Total
No anger
Most anger
Total


(b) Among those with no anger symptoms, what percentage had coronary heart disease? (Round the answer to one decimal place.)
%

(c) Among those with the most anger symptoms, what percentage had coronary heart disease? (Round the answer to one decimal place.)
%

(d) Does there appear to be an association between anger and the risk of coronary heart disease?
    

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Researchers studied a random sample of high school students who participated in interscholastic athletics to learn about the risk of lower-extremity injuries (anywhere between hip and toe) for interscholastic athletes. Of 992 participants in girls' soccer, 76 experienced lower-extremity injuries. Of 1670 participants in boys' soccer, 152 experienced lower-extremity injuries.
(a) Write a two-way table of observed counts for gender and whether a participant had a lower-extremity injury or not.

Gender Had Injury No Injury Total
Girls
Boys
Total


(b) Determine a two-way table of expected counts for these data. (Round the answers to one decimal place where it is needed.)
Gender Had Injury No Injury Total
Girls
Boys
Total


(c) Show calculations verifying that the value of the chi-square statistic is 1.66.

Chi-square = (76-85.0)2/ + (916- )2/907.0 + ( -143.0)2/143.0 + (1518- )2/ = 0.95 + 0.09 + + 0.05 = 1.66

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When 200 students were asked to pick a number from 1 to 10, the number of students selecting each number were as shown in the table.
Number 1 2 3 4 5 6 7 8 9 10 Total
Frequency 1 10 24 25 20 24 56 20 13 7 200
(a) What is the approximate probability that someone asked to pick a number from 1 to 10 will pick the number 6? (Round your answer to four decimal places.)


(b) What is the approximate probability that someone asked to pick a number from 1 to 10 will pick one of the two extremes, 1 or 10? (Round your answer to four decimal places.)


(c) What is the approximate probability that someone asked to pick a number from 1 to 10 will pick an odd number? (Round your answer to four decimal places.)

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In an election, 70% of the voters were Republicans, and 30% were not. Of the Republicans, 60% voted for Candidate X, and of the non-Republicans, 5% voted for Candidate X. Consider a randomly selected voter. Define A = Voter is Republican. B = Voted for Candidate X.
(a) Find the values. (Give the answers to two decimal places.)
P(A)
P(AC)
P(B|A)
P(B|AC)

(b) Find P(A and B). (Give the answer to three decimal places.)

Write in words what outcome it represents.
    


(c) Find P(AC and B). (Give the answer to four decimal places.)

Write in words what outcome it represents.
    


(d) Using the results in parts (b) and (c), find P(B). (Give the answer to four decimal places. Hint: The events in parts (b) and (c) cover all of the ways in which B can happen.)


(e) Use the result in part (d) to state what percent of the vote Candidate X received. (Give the answer to two decimal places.)
%

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Consider randomly drawing two students without replacement from a class of 45 students in which 4 are left-handed. Below is a tree diagram illustrating that the probability of selecting two left-handed students is 1/165. Calculate the probabilities labeled on the tree diagram. (Give answers as fractions.)
a =
b =
c =
d =
e =
h =
k =
m =
n =
w =

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A woman decides to have children until she has her first girl or until she has four children, whichever comes first. Let X = number of children she has. For simplicity, assume that the probability of a girl is .5 for each birth.
(a) The simple events in the simple space are {G, BG, BBG, BBBG, BBBB}, where we use B for boy and G for girl. For instance, one simple event is BG, because the woman quits once she has a girl. Find the probability for each of the simple events in the sample space.
P(G) =
P(BG) =
P(BBG) =
P(BBBG) =
P(BBBB) =

(b) Find the probability distribution function for X.
k 1 2 3 4
P(X = k)

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Assuming that X is a binomial random variable with n = 10 and p = 0.25, find the probability, P for each of the following values of X. (Round your answers to five decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
(a) X = 4.
P(X = 4) =

(b) X = 2.
P(X = 2) =

(c) X = 1.
P(X = 1) =

(d) X = 8.
P(X = 8) =


You may need to use the appropriate table in the Appendix of Tables to answer this question.

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Suppose the yearly rainfall totals for a some city follow a normal distribution, with mean of 29 inches and standard deviation of 10 inches. For a randomly selected year, what is the probability, P, that total rainfall will be in each of the following intervals? (Round all answers to four decimal places.)
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(a) Less than 19 inches.
P =

(b) Greater than 44 inches.
P =

(c) Between 19 and 39 inches.
P =

(d) Greater than 58 inches.
P =


You may need to use the appropriate table in the Appendix of Tables to answer this question.

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Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was 5 days, and the standard deviation of overall duration of symptoms was 1.2 days. For the placebo group, the mean overall duration of symptoms was 8.3 days, and the standard deviation was 2 days.
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(a) Calculate a 95% confidence interval for the mean overall duration of symptoms if everyone in the population were to take the zinc lozenges. (Round your answers to two decimal places.)
to days

(b) Calculate a 95% confidence interval for the mean overall duration of symptoms if everyone in the population were to take the placebo lozenges. (Round your answers to two decimal places.)
to days

(c) On the basis of the intervals computed in parts (a) and (b), is it reasonable to conclude generally that taking zinc lozenges reduces the overall duration of cold symptoms more than if taking a placebo? Explain why you think this is or is not an appropriate conclusion.
reasonable to conclude that taking zinc lozenges reduces the duration of symptoms. The confidence intervals computed in parts (a) and (b) , so a reasonable conclusion is that in a population of cold sufferers the mean duration of symptoms if zinc lozenges are taken is than the mean duration if placebo is taken.

(d) In their paper, the researchers say that they checked whether it was reasonable to assume that the data were sampled from a normal curve population and decided that it was. How is this relevant to the calculations done in parts (a) and (b)?
For relatively samples such as these, a necessary condition (in theory) is that the population of measurements has a normal distribution.


You may need to use the appropriate table in the Appendix of Tables to answer this question.

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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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Which of the following is not a continuous variable?
    

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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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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...."
    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 circle graphs.

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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?"

    This answer has not been graded yet.

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Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter a number.
Enter a number.
Enter a number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter an exact number.
Enter a fraction, integer, or exact decimal. Do not approximate.
Enter a fraction, integer, or exact decimal. Do not approximate.
Enter a fraction, integer, or exact decimal. Do not approximate.
Enter a fraction, integer, or exact decimal. Do not approximate.
Enter a fraction, integer, or exact decimal. Do not approximate.
Enter a fraction, integer, or exact decimal. Do not approximate.
Enter a fraction, integer, or exact decimal. Do not approximate.
Enter a fraction, integer, or exact decimal. Do not approximate.
Enter a fraction, integer, or exact decimal. Do not approximate.
Enter a fraction, integer, or exact decimal. Do not approximate.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter a number.
Enter an exact number.
Enter a number.