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Mendenhall et al-Intro to Probability & Stats 15/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 10 / 88

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

Last Saved : n/a Saving...  ()

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10/88 (11.4%)

  • Instructions

    Introduction to Probability and Statistics, 15th edition, by Mendenhall, Beaver, and Beaver, published by Cengage Learning, is a major overhaul from the previous edition, lowering the reading level, introducing concepts in a more intuitive way and significantly increasing homework scaffolding for difficulty level. Written in compliance with the GAISE college report, this text teaches students to become problem solvers who are adept at using technology to facilitate statistical reasoning as well as the interpretation of statistical results. Students will be able to describe real sets of data meaningfully, what the statistical tests mean in terms of their practical applications, how to evaluate the validity of the assumptions behind statistical tests and know what to do when statistical assumptions have been violated. The 15th edition contains 1884 exercises, employs real data throughout, and includes at least 75% new or updated examples. Introduction to Probability and Statistics, 15th edition, adds new sections on the uniform and exponential distributions, normal probability plots for assessing normality, best subsets regression procedures and binary logistic regression. The WebAssign component for this text engages students with an interactive eBook and several other resources.

    These questions show a variety of question types available in WebAssign for use with this title.

    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 asks students to answer multiple choice questions about pie charts.

    Question 4 asks students to think through a linear regression scenario then numerically enter statistics and a regression equation. Students can use SALT to answer this question.

    Question 5 asks students to answer multiple select questions about side-by-side boxplots.

    Question 6 walks students through the steps for a hypothesis test.

    Question 7 is a Simulation Question utilizing the JMP Applet.

    Question 8 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 9 is an example of a Statistical Lab. These activities support SPSS, Minitab, R, JMP, Excel, and TI 83/84 or TI-Inspire calculators.

    Question 10 highlights Milestone 1, the first step in presenting and tracking Project milestones for a statistical research project.

    Question 11 is a Concept Question where students are asked to provide a short answer to a prompt, then answer a multiple choice question about the same prompt, then reflect on their original answer.

    Question 12 provides assistance to students as they work through the steps for a hypothesis test. 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.

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.

1. 3/3 points  |  Previous Answers MendStat15 1.CE.001.CV. My Notes
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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) 17% and (b) 26%.
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) $105.
The dataset consists of data recorded across one semester including an index number that puts the observations in chronological order, the day of the week, and the total sales in dollars.
†http://jse.amstat.org/jse_data_archive.htm
Index Day of Week Sales($)
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) 70 inches (5'10") and (b) 84 inches (7'0").
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) 17% and (b) 26%.
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) $105.
The dataset consists of data recorded across one semester including an index number that puts the observations in chronological order, the day of the week, and the total sales in dollars.
†http://jse.amstat.org/jse_data_archive.htm
Index Day of Week Sales($)
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 70 inches (5'10") and (b) 84 inches (7'0").
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. seenKey

529
It looks like you selected Sports but answered the question associated with a different scenario. Click on the appropriate tab above and check your work. 		Incorrect: Your answer is incorrect. seenKey

78.3932
It looks like you selected Sports but answered the question associated with a different scenario. Click on the appropriate tab above and check your work. 		Incorrect: Your answer is incorrect. seenKey

3.4505
It looks like you selected Sports but answered the question associated with a different scenario. Click on the appropriate tab above and check your work. 		Incorrect: Your answer is incorrect. seenKey

78
It looks like you selected Sports but answered the question associated with a different scenario. Click on the appropriate tab above and check your work. 		Incorrect: Your answer is incorrect. seenKey

69
It looks like you selected Sports but answered the question associated with a different scenario. Click on the appropriate tab above and check your work. 		Incorrect: Your answer is incorrect. seenKey

89
It looks like you selected Sports but answered the question associated with a different scenario. Click on the appropriate tab above and check your work.
(b)
Create a histogram with "Starting Point" and "Bin/Class Width" values asked for.
The distribution for this variable Incorrect: Your answer is incorrect. seenKey

is

 mound shaped and Correct: Your answer is correct. seenKey

is

 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. seenKey

-2.43
Data value (b).
z = 
x − x
s
 
 = 
Data value (a) is Incorrect: Your answer is incorrect. seenKey

2.43

 standard deviations Incorrect: Your answer is incorrect. seenKey

below

 the mean whereas data value (b) is Incorrect: Your answer is incorrect. seenKey

1.62

 standard deviations Incorrect: Your answer is incorrect. seenKey

above

 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. seenKey

68.04
Find the data value with a z-score of 3, rounded to two decimal places.
x = z · s + x
 =  Incorrect: Your answer is incorrect. seenKey

88.74
Our sample's minimum value Incorrect: Your answer is incorrect. seenKey

is not

 further than 3 standard deviations below the mean. Our sample's maximum further than 3 standard deviations above the mean. Upon further inspection of the histogram in SALT it can be observed that observations would have a z-score between −3 and 3.


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When you were growing up, did you feel that you did not have enough free time? Parents and children have differing opinions on this subject. A research group surveyed 198 parents and 200 children and recorded their responses to the question, "How much free time does your child have?" or "How much free time do you have?" The responses are shown in the table below.
Just the
Right Amount 		Not
Enough 		Too
Much 		Don't
Know
Parents 138 14 40 6
Children 130 48 16 6
(a) Define the sample and the population of interest to the researchers.
    

(b) Describe the variables that have been measured in this survey. Are the variables qualitative or quantitative? Are the data univariate or bivariate?
    

(c) What do the entries in the cells represent?
    

(d) Use comparative pie charts to compare the responses for parents and children.

(e) What other graphical techniques could be used to describe the data? Would any of these techniques be more informative than the pie charts constructed in part (d)?

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Male crickets chirp by rubbing their front wings together. They chirp faster with increasing temperature and slower with decreasing temperatures. The following table shows the number of chirps per second for a cricket, recorded at 10 different temperatures.
Chirps per second 23 19 22 21 21 19 17 20 18 19
Temperature 88 73 91 85 82 75 69 82 69 83
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Which of the two variables (temperature and number of chirps) is the independent variable, x?
     Correct: Your answer is correct.
Which of the two variables (temperature and number of chirps) is the dependent variable, y?
     Incorrect: Your answer is incorrect.
(b)
Plot the data using a scatterplot.

How would you describe the relationship between temperature and number of chirps?
    
(c)
Find the least-squares line relating the number of chirps to the temperature. (Round your numeric values to three decimal places.)
y =
(d)
If a cricket is monitored at a temperature of 86 degrees, what would you predict his number of chirps would be? (Round your answer to the nearest whole number.)
chirps
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Researchers analyzed the percentage of aluminum oxide in 26 samples of Romano-British pottery found at four different kiln sites in the United Kingdom.† Since one of the sites only provided two measurements, that site is eliminated, and comparative box plots of aluminum oxide at the other three sites are shown.
A comparative box plot made of 3 box plots has a horizontal axis labeled "Aluminum Oxide" numbered from 10 to 22.
  • The box plot labeled "Site A" occurs first. The left whisker is approximately 14.8, the left edge of the box is approximately 15.8, the line inside the box is approximately 17.8, the right edge of the box is approximately 18.8, and the right whisker is approximately 19.2.
  • The box plot labeled "Site I" occurs next. The left whisker is approximately 15.8, the left edge of the box is approximately 17, the line inside the box is approximately 18, the right edge of the box is approximately 19.6, and the right whisker is approximately 20.8.
  • The box plot labeled "Site L" occurs last. The left whisker is approximately 10.2, the left edge of the box is approximately 11.6, the line inside the box is approximately 12.6, the right edge of the box is approximately 13.8, and the right whisker is approximately 14.6.
(a)
What two variables have been measured in this experiment? Are they qualitative or quantitative? (Select all that apply.)
Correct: Your answer is correct.

(b)
Compare the amount of aluminum oxide in the samples at the three sites. (Select all that apply.)
Incorrect: Your answer is incorrect.

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A company was contemplating the installation of a flextime schedule in which a worker schedules his or her work hours or compresses work weeks. The company estimates that it needs a minimum mean of 7 hours per day per assembly worker in order to operate effectively. Each of a random sample of 80 of the company's assemblers was asked to submit a tentative flextime schedule. If the mean number of hours per day for Monday was 6.7 hours and the standard deviation was 2.3 hours, do the data provide sufficient evidence to indicate that the mean number of hours worked per day on Mondays, for all of the company's assemblers, will be less than 7 hours? Test using α = 0.05.

State the null and alternative hypotheses.
    

Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)
test statistic     z = Incorrect: Your answer is incorrect. seenKey

-1.17
rejection region     z >
    z <

State your conclusion.
     Incorrect: Your answer is incorrect.

You may need to use the appropriate appendix table or technology to answer this question.
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The following JMP output contains information on 133 movies released in 2011. Data on domestic gross (the income from the film in the U.S. in millions of dollars), production budget (in millions of dollars), and movie genre (action, adventure, etc.) were considered. Use the JMP output to answer the questions below.

  • JMP Applet

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Stats in Practice: Correlation and Regression

  • Part I - Multiple Choice Questions

    The video discusses a survey conducted by FreeCreditScore.com that found that when choosing a long term partner, respondents ranked financial responsibility as important as what characteristic of the potential partner?
         Correct: Your answer is correct.
    Correct. The video says that respondents ranked financial responsibility as important as physical attractiveness and compatibility when choosing a long term partner.
    What type of variable is a credit score?
         Correct: Your answer is correct.
    Correct. A credit score is a number, usually between 300 and 800, depending on which credit score is being used. This is a quantitative variable in that, for example, taking an average makes sense. A qualitative variable, also called a categorical variable, describes an entity by placing it into a category or group, such as male or female.
    A positive correlation (or relationship) between two variables means that as one increases, the other increases. In contrast, a negative correlation means that as one increases, the other decreases. If a higher credit score indicates a better credit history, then the video implies that the correlation between credit scores of a partner and the number of years the relationship with that partner lasts ("relationship longevity") is which of the following?
         Correct: Your answer is correct.
    Correct. The video implies that a better credit score suggests a person is more responsible, and that one would expect greater relationship longevity with a more responsible person. This describes a positive relationship between these two quantitative variables.

  • Part II - Discussion Question

    Describe a quantitative variable not mentioned in the video that you would expect to have a positive relationship with a person's credit score. That is, people who tend to have higher credit scores also tend to have higher values of your selected variable. Describe why you are guessing that the relationship between credit score and your chosen variable is positive.

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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 2013–November, 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.
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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?"

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Concept Question
Car insurance rates for teenagers are generally higher than insurance rates for adult drivers.
Part 1 of 3
If car insurance rates for teenagers are approximately normally distributed with a standard deviation of $640 per year, find the mean insurance rate for teenagers if 10.56% of teenagers pay more than $2,000 annually for car insurance. (Use a table or technology. Round your answer to the nearest dollar.)

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What is normal, when it comes to people's body temperatures? A random sample of 130 human body temperatures had a mean of 98.15° and a standard deviation of 0.73°. Does the data indicate that the average body temperature for healthy humans deviates from 98.6°, the usual average temperature cited by physicians and others? Test using both methods given in this section.
(a)
Use the p-value approach with α = 0.05.
State the null and alternative hypothesis.
    
Find the test statistic and the 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)
Use the critical value approach with α = 0.05.
Find the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)
z > z <
State your conclusion.
    
(c)
Compare the conclusions from parts (a) and (b). Are they the same?
    
(d)
The 98.6° standard was derived by a German doctor in 1868, who claimed to have recorded 1 million temperatures in the course of his research.† What conclusions can you draw about his research in light of your conclusions in parts (a) and (b)?
    
You may need to use the appropriate appendix table or technology to answer this question.

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