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Illowsky and Dean - Intro Stats 1/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 30 / 103

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

Last Saved : n/a Saving...  ()

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  • Instructions

    Introductory Statistics, 1st edition, authored by Barbara Illowsky and Susan Dean of De Anza College, is available through OpenStax and is now supported by homework questions and student learning resources within WebAssign.

    Added for Spring 2021! Question 1 is an example of a Statistical Lab.

    Question 2 exemplifies submitting an incorrect response, settings can allow students to have rhetorical guidance on answering the question.

    Question 3 contains an image with answer blanks included for a seamless experience for the student.

    Question 4 is a multipart question in which students are asked to analyze the given information to determine the necessary distribution and then use that distribution to determine probabilities.

    Question 5 is a multipart question that uses multiple answer types for students to graph the probability distribution, derive its formula, and then use that formula to determine probabilities.

    Question 6 utilizes multiple answer types to determine probability statements, graph the respective areas, and then determine probabilities.

    Question 7 requires students to construct a confidence interval.

    Question 8 guides students through a hypothesis test using the Student's t distribution.

    Question 9 steps students through a hypothesis test using the Chi-Square distribution.

    Question 10 showcases the use of some values from an ANOVA table to calculate the F test statistic. 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.

1. 3/12 points  |  Previous Answers IllowskyIntroStat1 2.Lab.003.Excel. My Notes
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Statistical Lab

  • Background

    In July of 2010, two reporters writing for the Los Angeles Times broke a story about the city of Bell, one of the poorest and smallest cities in Los Angeles County. The two highest paid city officials, Manager Robert Rizzo and Assistant City Manager Angela Spaccia, pulled in salaries that seemed much higher than similar officials working in much larger, wealthier cities in the United States. Further investigation uncovered many instances of corruption among several of the city managers and city leaders, including instances of council members being paid thousands of dollars to attend meetings that lasted no longer than a few minutes.
    Preliminary Hearing of Bell City Manager Robert Rizzo
    A close-up of Bell City Manager Robert Rizzo at his preliminary hearing.
    For the purposes of this lab, you are retracing the steps of an investigative reporter who broke the story by examining the salaries of public employees working for Bell and another city of comparable size and location.

  • Guidelines

    In this lab, you will do the following.
    • Compute the mean and median to get a sense of how much a typical public employee earns in these cities.
    • Calculate the standard deviation, and determine how much variation there is in public employee salaries.
    • Look for any extreme outliers in public employee salaries, using the standard deviation.

  • About the Data

    For this lab, you need to download the bellemployeesalaries.csv dataset. The data comes from the California State Controller's database, which contains information on the salary and other compensation benefits of public employees in the cities, counties, and special districts of California. The data you will be using shows the 2009 salaries of paid public employees (working more than 25 hours per week) for the cities of Bell and Duarte. Each row in the file represents a paid public employee. The file contains four columns:
    • cityName—the name of the city where the employee works; in this data file, the city will be either Bell or Duarte
    • department—the department name where the city employee worked
    • position—the job title of the city employee
    • wages—the total amount the employee earned in the year 2009 in US dollars, including their base pay and overtime

  • Tech Guide

    You will need to use the Excel Tech Guide.

  • Lab Questions

    Create and upload a histogram of the salary data for the city of Bell, where each bar width is about 50,000 US dollars. (Submit a file with a maximum size of 1 MB.)
    achieve_for_statistics_pie_charts copy.png

    This answer has not been graded yet.

    (a)
    Is the distribution of the salaries symmetric?
         Correct: Your answer is correct.
    (b)
    Without making any calculations, will the mean be larger or smaller than the median? Explain why.
    The mean will be Correct: Your answer is correct. than the median, because the distribution is Correct: Your answer is correct. .
    For the city of Duarte, the median salary is 31,597.00 US dollars, the mean salary is 44,713.88 US dollars, and the standard deviation of the salaries is 36,448.59 US dollars (using the formula for the population standard deviation—recall that the data contains the salaries of all city employees). To ensure that your software tool is using the correct formulas, verify these results.
    (a)
    What is the population median, mean, and standard deviation for the salaries in Bell? (Round your answers to two decimal places.)
    Mean (μ) $
    Enter a number.
         Median $
    Enter a number.
         Standard Deviation (σ) $
    Enter a number.
    (b)
    Compare the mean salaries of Bell and Duarte, paying attention to the position titles and salaries in the two cities.
    The mean salary in Bell is the mean salary in Duarte.
    Does it pay to be a police officer in Bell?

    This answer has not been graded yet.

    In general, city managers earn the highest salaries in a city, and are paid well above a typical city employee. We want to find how far away the city manager salaries are from the mean for each city. Some cities have more variation in salaries than others, so we will compute how far the highest paid salaries are from the mean, and then divide that difference by the standard deviation of the city salaries, in order to make a fair comparison. In other words, we are going to calculate how many standard deviations the highest salaries are from their city means. Use the following formula.
    (Highest Salary − Mean Salary)
    Standard Deviation
    (a)
    For the city of Bell, how many standard deviations is the highest salary from the mean? (Round your answer to four decimal places.)
    Enter a number.
    (b)
    For the city of Duarte, how many standard deviations is the highest salary from the mean? (Round your answer to four decimal places.)
    Enter a number.
    (c)
    As an investigative reporter, you are used to seeing city manager salaries 4 or even 5 standard deviations away from the mean. What do you find curious about this data?

    This answer has not been graded yet.

  • References

    1. Gottlieb, Jeff and Vives, Ruben, Los Angeles Times, "Is A City Manager Worth $800,000?," July 15, 2010, http://articles.latimes.com/2010/jul/15/local/la-me-bell-salary-20100715.
    2. Gottlieb, Jeff, Los Angeles Times, "Bell Sues Ex-Councilman, Foundation and Construction Firm Over Payouts," June 24, 2014, http://www.latimes.com/local/la-me-0625-bell-lawsuit-20140625-story.html.
    3. Knoll, Corina and Gottlieb, Jeff, Los Angeles Times, "Rizzo Gets 12 Years in Prison, Marking End to Scandal that Rocked Bell," April 16, 2014, http://www.latimes.com/local/lanow/la-me-ln-rizzo-set-to-be-sentenced--20140415-story.html.
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2. 4/6 points  |  Previous Answers IllowskyIntroStat1 1.1.043.HW. My Notes
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4/6
 
Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally. Define the following in terms of the study. Give examples where appropriate.

  • Part (a)

    The population
        

  • Part (b)

    The sample
         Correct: Your answer is correct.
    Correct! A group of children taking lessons represents a subset of the entire population of children taking lessons.

  • Part (c)

    The parameter
         Correct: Your answer is correct.
    Correct! The average age of all children when they take their first lesson represents the topic of interest of the population.

  • Part (d)

    The statistic
         Correct: Your answer is correct.
    Correct! The average age of a group of children is a summary measure of a sample.

  • Part (e)

    The variable
         Correct: Your answer is correct.
    Correct! The characteristic of interest is the age of each child.

  • Part (f)

    The data
         Incorrect: Your answer is incorrect.

    Incorrect. The number of lessons does not represent the variable of interest.


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3. 14/14 points  |  Previous Answers IllowskyIntroStat1 3.5.116.HW. My Notes
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14/14
 
A box of cookies contains 3 chocolate and 7 butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. (How many cookies did he take?)

  • Part (a)

    Draw the tree that represents the possibilities for the cookie selections. Write the probabilities along each branch of the tree. (Let B be the event that he selected a butter cookie, and let C be the event that he selected a chocolate cookie. Enter your probabilities as fractions.)
    WebAssign Plot
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.

  • Part (b)

    Are the probabilities for the flavor of the second cookie that Miguel selects independent of his first selection? Explain.
         Incorrect: Your answer is incorrect.

    Incorrect. This reasoning is incorrect, if selecting a chocolate cookie second is not affected by the first selection, then the events would be independent, not dependent.

  • Part (c)

    For each complete path through the tree, write the event it represents and find the probabilities. (Enter your probabilities as fractions.)
    P(BB) =
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.
    P(BC) =
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.
    P(CB) =
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.
    P(CC) =
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.

  • Part (d)

    Let S be the event that both cookies selected were the same flavor. Find P(S). (Enter your probability as a fraction.)
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.

  • Part (e)

    Let T be the event that both cookies selected were different flavors. Find P(T) by two different methods: by using the complement rule and by using the branches of the tree. Your answers should be the same with both methods. (Enter your probability as a fraction.)
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.

  • Part (f)

    Let U be the event that the second cookie selected is a butter cookie. Find P(U). (Enter your probability as a fraction.)
    Enter a fraction, integer, or exact decimal. Do not approximate.
     Correct: Your answer is correct.


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4. 5/10 points  |  Previous Answers IllowskyIntroStat1 4.3.095.HW. My Notes
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5/10
 
More than 96 percent of the very largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 17 such institutions. We are interested in the number that offer distance learning courses.

  • Part (a)

    In words, define the Random Variable X.
         Correct: Your answer is correct.
    Correct! This is a numerical measure of the outcome of the study.

  • Part (b)

    List the values that X may take on.
         Correct: Your answer is correct.

  • Part (c)

    Give the distribution of X. (Enter exact numbers as integers, fractions, or decimals.)
    X ~ Correct: Your answer is correct.
    Enter an exact number.
     Correct: Your answer is correct. ,
    Enter a number.
     Correct: Your answer is correct.

  • Part (d)

    On average, how many schools would you expect to offer such courses? (Round your answer to the nearest whole number.)
    Enter a number.
     schools

  • Part (e)

    Find the probability that at most fifteen offer such courses. (Round your answer to four decimal places.)
    Enter a number.

  • Part (f)

    Is it more likely that 16 or that 17 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.
    The probability that 16 schools will offer such courses is and the probability that 17 schools will offer such courses is . Therefore, it is more likely that schools will offer distance learning courses.


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5. 4/13 points  |  Previous Answers IllowskyIntroStat1 5.2.075.HW. My Notes
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4/13
 
For each probability and percentile problem, draw the picture.

A random number generator picks a number from 1 to 8 in a uniform manner.

  • Part (a)

    Give the distribution of X.
    X ~
    Answer is not case sensitive.
     Correct: Your answer is correct.
    Enter an exact number.
     Correct: Your answer is correct. ,
    Enter an exact number.
     Correct: Your answer is correct.

  • Part (b)

    Graph the probability distribution.

    Correct: Your answer is correct.

  • Part (c)

    Enter an exact number as an integer, fraction, or decimal.
    f(x) =
    		,    where
    Enter an exact number.
     ≤ x ≤
    Enter an exact number.

  • Part (d)

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

  • Part (e)

    Round your answer to two decimal places.
    σ =
    Enter a number.

  • Part (f)

    Enter an exact number as an integer, fraction, or decimal.
    P(3.75 < x < 7.5) =

  • Part (g)

    Round your answer to two decimal places.
    P(x > 5.67) =
    Enter a number.

  • Part (h)

    Enter an exact number as an integer, fraction, or decimal.
    P(x > 5 | x > 3) =

  • Part (i)

    Find the 80th percentile. (Round your answer to one decimal place.)
    Enter a number.


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6. –/13 points IllowskyIntroStat1 6.2.073.HW. My Notes
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–/13
 
According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual.

  • Part (a)

    Give the distribution of X.
    X ~
    Enter an exact number.
     ,
    Enter a number.

  • Part (b)

    Find the probability that the person is between 64 and 69 inches.

    Write the probability statement.
    P 
    Enter an exact number.
     < X <
    Enter an exact number.


    What is the probability? (Round your answer to four decimal places.)
    Enter a number.

    Sketch the graph.

  • Part (c)

    Would you expect to meet many Asian adult males over 72 inches? Explain why or why not, and justify your answer numerically.
    , because the probability that an Asian male is over 72 inches tall is
    Enter a number.
     .

  • Part (d)

    The middle 40% of heights fall between what two values?

    Write the probability statement.
    P(x1 < X < x2) =
    Enter a number.


    State the two values. (Round your answers to one decimal place.)
    x1 =
    Enter a number.
    x2 =
    Enter a number.

    Sketch the graph.

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The Federal Election Commission (FEC) collects information about campaign contributions and disbursements for candidates and political committees each election cycle. A political action committee (PAC) is a committee formed to raise money for candidates and campaigns. A Leadership PAC is a PAC formed by a federal politician (senator or representative) to raise money to help other candidates' campaigns.

The FEC has reported financial information for 556 Leadership PACs that operated during one election cycle. The following table shows the total receipts during this cycle for a random selection of 30 Leadership PACs.
$46,501.00 $0 $40,966.50 $105,889.20 $5,176.00
$29,052.00 $19,499.00 $181,558.20 $31,502.00 $149,972.80
$2,555,365.20 $12,024.00 $408,998.00 $60,521.70 $18,002.00
$61,812.20 $76,530.80 $119,461.20 $0 $63,522.00
$6,501.00 $502,579.00 $705,062.10 $708,257.90 $135,811.00
$2,001.00 $2,002.00 $0 $1,287,935.80 $219,148.30
x = $251,855.06
s = $521,130.58
Use this sample data to construct a 96% confidence interval for the mean amount of money raised by all Leadership PACs during the election cycle. Use the Student's t-distribution. (Round your answers to the nearest cent.)
Enter a number.
 ,
Enter a number.
dollars
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8. –/18 points IllowskyIntroStat1 9.5.074.HW. My Notes
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–/18
 
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 31 tires surveyed, the mean lifespan was 46,800 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim?

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

  • Part (a)

    State the null hypothesis.
        

  • Part (b)

    State the alternative hypothesis.
        

  • Part (c)

    In words, state what your random variable X represents.
        

  • Part (d)

    State the distribution to use for the test. (Round your answers to two decimal places.)
    X
     ~
    Answer is not case sensitive.
    Enter an exact number.
     ,
    Enter a number.

  • Part (e)

    What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)
    =
    Enter a number.

  • Part (f)

    What is the p-value? (Round your answer to four decimal places.)
    Enter a number.

    Explain what the p-value means for this problem.
        

  • Part (g)

    Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

  • Part (h)

    Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
    (i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
    α =
    Enter a number.

    (ii) Decision:
        

    (iii) Reason for decision:
        

    (iv) Conclusion:
        

  • Part (i)

    Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to the nearest whole number.)
    WebAssign Plot
    Enter a number.
    Enter a number.
    Enter a number.


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A plant manager is concerned her equipment may need recalibrating. It seems that the actual weight of the 15 oz. cereal boxes it fills has been fluctuating. The standard deviation should be at most 0.5 oz. In order to determine if the machine needs to be recalibrated, 89 randomly selected boxes of cereal from the next day's production were weighed. The standard deviation of the 89 boxes was 0.52. Does the machine need to be recalibrated? Conduct a hypothesis test at the 5% level.

  • Part (a)

    State the null hypothesis.
        

  • Part (b)

    State the alternative hypothesis.
        

  • Part (c)

    What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)
    Enter an exact number.

  • Part (d)

    State the distribution to use for the test.
        

  • Part (e)

    What is the test statistic? (Round your answer to two decimal places.)
    Enter a number.

  • Part (f)

    What is the p-value? (Round your answer to four decimal places.)
    Enter a number.

    Explain what the p-value means for this problem.
        

  • Part (g)

    Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.

  • Part (h)

    Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write the appropriate conclusion.
    (i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
    α =
    Enter a number.

    (ii) Decision:
        

    (iii) Reason for decision:
        

    (iv) Conclusion:
        


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Three different traffic routes are tested for mean driving time. The entries in the table are the driving times in minutes on the three different routes. The one-way ANOVA results are shown in the table below.
Route 1 Route 2 Route 3
29 27 16
32 28 41
27 28 22
35 36 31
State
SSbetween.
 (Round your answer to one decimal place.)
Enter a number.

State
SSwithin.
 (Round your answer to one decimal place.)
Enter a number.

State the F statistic. (Round your answer to four decimal places.)
Enter a number.

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