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Question: The state of California defines family income


The state of California defines family income groups in terms of median county income as follows:
Extremely low income: below 30% of county median income
Very low income: between 30% and 50% of county median income
Low income: between 50% and 80% of county median income Moderate income: between 80% and 120% of county median income For San Luis Obispo County, the median income as of May 24, 2016 for single person households was $53,950 (www.slocounty.ca.gov/assets/Pl/housing/ahS/ahS.pdf, august 1, 2016, retrieved april 19, 2017).
a. Interpret the value of the median income for a singleperson household in San Luis Obispo County.
b. Each of the following statements is incorrect. For each statement, use the given information to explain why it is incorrect.
Statement 1: 30% of the single-person households in San Luis Obispo County would be classified as extremely low income.
Statement 2: More than 50% of the single-person households in San Luis Obispo County would be classified as extremely low income or very low income.
Statement 3: There cannot be any single-person households in San Luis Obispo County that would be classified as having an income that was greater than those in the moderate income category.


> Data on tipping percent for 20 restaurant tables, consistent with summary statistics given in the paper “beauty and the labor Market: evidence from restaurant Servers” (unpublished manuscript by Matt Parrett, 2007), ar

> The press release “Men need to Man Up, according to ball Park brand Survey” (PR Newswire, October 14, 2015) describes the results of a study in which 1012 U.S. men were asked a number of questions about “life’s tough conversations.” One result from this

> The following conclusion from a statistical study appeared in the article “Smartphone nation” (AARP Bulletin, September 2009): “If you love your smartphone, you’re far from alone. Half of all boomers sleep with their cell phone within arm’s length. Two o

> The report “education Pays: how college Shapes lives” (trends.collegeboard.org/sites/default/files/education -pays-how-college-shapes-lives-report-022714.pdf, retrieved april 20, 2017) gave the following percentiles for annual earnings in 2011 for full-t

> The accompanying table gives the mean and standard deviation of reaction times (in seconds) for each of two different stimuli: Suppose your reaction time is 4.2 seconds for the first stimulus and 1.8 seconds for the second stimulus. Compared to other pe

> Fiber content (in grams per serving) and sugar content (in grams per serving) for 18 high-fiber cereals (www .consumerreports.com) are shown. Fiber Content Sugar Content a. Find the median, quartiles, and interquartile range for the fiber content data

> The report “Most licensed Drivers age 851: States” (www. bloomberg.com/graphics/best-and-worst/#most-licenseddrivers-age-85-plus-states, retrieved april 20, 2017) gives the percentage of drivers in each state and the D

> The accompanying data are a subset of data read from a graph in the paper “ladies First? a Field Study of Discrimination in coffee Shops” (Applied Economics, april 2008). The data are wait times (in seconds) between o

> The insurance institute for highway Safety (www.iihs.org, June 11, 2009) published data on repair costs for cars involved in different types of accidents. In one study, seven different 2009 models of mini- and micro-cars were driven at 6 miles per hour s

> Data on tipping percent for 20 restaurant tables, consistent with summary statistics given in the paper “beauty and the labor Market: evidence from restaurant Servers” (unpublished manuscript by Matt Parrett, 2007), ar

> The paper “caffeinated energy Drinks—a growing Problem” (Drug and Alcohol Dependence [2009]: 1–10) reported caffeine per ounce for 8 top-selling energy drinks and for 11 highcaffeine

> The accompanying data are consistent with summary statistics from the paper “Shape of glass and amount of alcohol Poured: comparative Study of effect of Practice and concentration” (British Medical Journal [2005]: 1512

> Data on a customer satisfaction rating (called the APEAL rating) are given for each brand of car sold in the United States (USA TODAY, March 29, 2016). The APEAL rating is a score between 0 and 1,000, with higher values indicating greater satisfaction. C

> For each of the following data sets, construct a graphical display of the data distribution and then indicate what summary measures you would use to describe center and variability. a. The following are data on weekend exercise time for 20 females consi

> Suppose that the distribution of scores on an exam is mound shaped and approximately symmetric. The exam scores have a mean of 100 and the 16th percentile is 80. a. What is the 84th percentile? b. What is the approximate value of the standard deviation

> The mean reading speed of students completing a speed-reading course is 450 words per minute (wpm). If the standard deviation is 70 wpm, find the z-score associated with each of the following reading speeds. a. 320 wpm b. 475 wpm c. 420 wpm d.

> Suppose that the distribution of weekly water usage for single-family homes in a particular city is mound shaped and approximately symmetric. The mean is 1400 gallons, and the standard deviation is 300 gallons. a. What is the approximate value of the 16

> The mean number of text messages sent per month by customers of a cell phone service provider is 1650, and the standard deviation is 750. Find the z-score associated with each of the following numbers of text messages sent. a. 0 b. 10,000 c. 4500 d. 3

> The following data values are the 2014 per capita operating expenditures on public libraries for each of the 50 U.S. states and Washington, D.C. (from www.imls.gov /research-evaluation/data-collection/public-libraries-survey /explore-pls-data, retrieved

> Suppose that your younger sister is applying to college and has taken the SAT exam. She scored at the 83rd percentile on the verbal section of the test and at the 94th percentile on the math section. Because you have been studying statistics, she asks yo

> In a study investigating the effect of car speed on accident severity, the vehicle speed at impact was recorded for 5000 fatal accidents. For these accidents, the mean speed was 42 mph and the standard deviation was 15 mph. A histogram revealed that the

> Suppose that your statistics professor returned your first midterm exam with only a z-score written on it. She also told you that a histogram of the scores was mound shaped and approximately symmetric. How would you interpret each of the following z-scor

> Explain why the following graphical display (similar to a graph that appeared in USA TODAY, September 17, 2009) is misleading. U.S. currency tainted by cocaine Among 234 U.S. bills from 17 large U.S. cities, percentage with cocaine traces: 90% FEDERA

> The paper “Study of the Flying ability of Rhynchophorus ferrugineus adults using a computer-Monitored Mill” (Bulletin of Entomological Research [2014]: 462–467) summarized data from a study of red pal

> The report “who borrows Most? bachelor’s Degree recipients with high levels of Student Debt” (trends .collegeboard.org/content/who-borrows-most-bachelors -degree-recipients-high-levels-student-debt-april-2010, retrieved april 20, 2017) included the follo

> The mean playing time for a large collection of compact discs is 35 minutes, and the standard deviation is 5 minutes. a. What value is 1 standard deviation above the mean? One standard deviation below the mean? What values are 2 standard deviations away

> A student took two national aptitude tests. The mean and standard deviation were 475 and 100, respectively, for the first test, and 30 and 8, respectively, for the second test. The student scored 625 on the first test and 45 on the second test. Use z-sco

> Refer to the data given in the previous exercise. a. Are there any outliers in the inflation-adjusted gross movie income data? If so, which data values are outliers? b. Construct a boxplot for the inflation-adjusted gross movie income data. c. For the

> The Bloomberg web site included the data in the accompanying table on the number of movies made by 25 Saturday Night Live cast members as of 2014 (www.bloomberg.com/graphics/best-and-worst/#top-grossing-saturday -night-live-alumni, retrieved april 20, 20

> The U.S. Department of Health and Human Services reported the estimated percentage of households with only wireless phone service (no landline) in 2014 for the 50 states and the District of Columbia (DC) (cdc.gov/nchs/data /nhis/earlyrelease/wireless_sta

> A graph similar to the one below appeared in the paper “Does the weight of the Dish influence our Perception of Food?” (Food Quality and Preference, [2011]: 753–756). The graph was constructed using d

> Like many people, dogs can also suffer from back problems. Animal researchers were interested in learning whether laser therapy after back surgery would shorten recovery time for dogs that needed back surgery (“lowlevel laser therapy re

> The article “the best—and worst—Places to be a working woman” (The Economist, graphic Detail for March 3, 2016) reported values of what it calls the glass-ceiling index, which is des

> The following two graphical displays are similar to ones that appeared in USA TODAY (June 1, 2009 and July 28, 2009). One is an appropriate representation and the other is not. For each of the two, explain why it is or is not drawn appropriately.

> The accompanying data are the percentage of babies born prematurely in 2014 for the 50 U.S. states and the District of Columbia (DC) (the henry J. Kaiser Family Foundation, kff.org/other/state-indicator/preterm-births-by -raceethnicity/, retrieved april

> The accompanying data are a subset of data read from a graph in the paper “ladies First? a Field Study of Discrimination in coffee Shops” (Applied Economics [april, 2008]). The data are the waiting time (in seconds) be

> The accompanying data are median ages for residents of each of the 50 U.S. states and the District of Columbia (DC) in 2014 (the Statistics Portal, retrieved May 18, 2016 from www.statista.com/statistics/208048/median -age-of-population-in-the-usa-by-sta

> The accompanying data are consistent with summary statistics that appeared in the paper “Shape of glass and amount of alcohol Poured: comparative Study of effect of Practice and concentration” (British Medical Journal

> The National Climate Data Center gave the accompanying annual rainfall (in inches) for Medford, Oregon, from 1950 to 2014 (www.ncdc.noaa.gov/cdoweb/datasets#annual, retrieved april 20, 2017): a. Calculate the quartiles and the interquartile range. b. Ar

> Data on the gasoline tax per gallon (in cents) in 2015 for the 50 U.S. states and the District of Columbia (DC) are shown below (www.eia.gov/tools/faqs/faq.cfm?id=10&t=10, retrieved September 1, 2016). a. The smallest value in the data set is 9.0 (A

> The data below are manufacturing defects per 100 cars for the 30 brands of cars sold in the United States (USA TODAY, March 29, 2016). Many of these values are larger than 100 because one car might have many defects. Use these data to construct a boxplo

> The u.S. environmental Protection agency reported the following sulphur dioxide emissions (in tons) for the 48 states in the continental United States (www3.epa .gov/airmarkets/progress/reports/emissions_reductions_so2 .html#figure2, retrieved april 20,

> A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the following data on time (in seconds) to complete the escape (“oxygen consumption and ventilation During escape from an offshore Platform,&acir

> The following gasoline tax per gallon data for each of the 50 U.S. states and the District of Columbia (DC) in 2015 were obtained from the U.S. Energy Information Administration (www.eia.gov/tools/faqs/faq.cfm?id=10&t=10, retrieved April 17, 2017).

> The article “Fliers Trapped on Tarmac Push for Rules on Release” (USA TODAY, July 28, 2009) gave the following data for 17 airlines on the number of flights that were delayed on the tarmac for at least 3 hours for the

> An article about college loans (“New Rules Would Protect Students,” USA TODAY, June 16, 2010) reported the percentage of students who had defaulted on a student loan within 3 years of when they were scheduled to begin

> The article “Where College Students Buy Textbooks” (USA TODAY, October 14, 2010) gave data on where students purchased books. The accompanying frequency table summarizes data from a sample of 1152 full-time college stu

> To compare the amount of money men and women spent on their most recent haircut, each person in a sample of 20 women and each person in a sample of 20 men was asked how much was spent on his or her most recent haircut. Required: 1. How many variables a

> To learn about where students purchase textbooks, each student in a random sample of 200 students at a particular college was asked to select one of the following responses: campus bookstore, off-campus bookstore, purchased all books online, or used a co

> The accompanying graphical display is from the Fall 2008 Census Enrollment Report at Cal Poly, San Luis Obispo. It uses both a pie chart and a segmented bar graph to summarize ethnicity data for students enrolled in Fall 2008. a. Use the information in

> To see if satisfaction level differs for airline passengers based on where they sit on the airplane, all passengers on a particular flight were surveyed at the end of the flight. Passengers were grouped based on whether they sat in an aisle seat, a middl

> To learn about how number of hours worked per week and number of hours spent watching television in a typical week are related, each person in a sample of size 40 was asked to keep a log of hours worked and hours spent watching television for one week. A

> To learn about credit card debt of students at a college, the financial aid office asks each student in a random sample of 75 students about his or her amount of credit card debt. Required: 1. How many variables are in the data set? 2. Is the data set c

> In a survey of 100 people who had recently purchased motorcycles, data on the following variables were recorded: Gender of purchaser Brand of motorcycle purchased Number of previous motorcycles owned by purchaser Telephone area code of purchaser Weight o

> The accompanying graphical display is similar to one that appeared in the USA TODAY Snapshots collection (www.usatoday.com/picture-gallery/news/2015/04/07 /usa-today-snapshots/6340793/, retrieved October 13, 2016). The graph is meant to represent respons

> The following graphical display is similar to one that appeared in USA TODAY (August 3, 2009) and is meant to be a comparative bar graph. Do you think it is an effective summary of the data? If so, explain why. If not, explain why not and construct a dis

> The following display is similar to one that appeared in USA TODAY (May 16, 2011). It is meant to display responses to the question shown. a. Explain how this display may be misleading. b. Construct a pie chart or a bar chart that accurately summarizes t

> The accompanying graph is similar to one that appears in the USA TODAY Snapshots collection (www.usatoday.com/picture-gallery /news/2015/04/07/usa -today-snapshots/6340793/, retrieved October 13, 2016). This graph was intended to show the change in the a

> The accompanying graph is similar to one that appeared in USA TODAY (August 5, 2008). This graph is a modified comparative bar graph. The modifications (incorporating hands and the earth) were most likely made to construct a display that readers would fi

> The graphical display at the top left of the next page is similar to one that appeared in USA TODAY (October 22, 2009). It summarizes survey responses to a question about visiting social networking sites while at work. Which of the graph types introduced

> The article “the wedding industry’s Pricey little Secret” (June 12, 2013, www.slate.com, retrieved april 19, 2017) stated that the widely reported average wedding cost is grossly misleading. The article reports that in 2012, the average wedding cost was

> The accompanying comparative segmented bar charts are similar to ones appearing in the report “The Future of the First Amendment: 2014 Survey of High School Students and Teachers” (www.knightfoundation .org/future-firs

> The Center for Science in the Public Interest evaluated school cafeterias in 20 school districts across the United States. Each district was assigned a numerical score on the basis of rigor of food codes, frequency of food safety inspections, access to i

> The following display is similar to one that appeared in USA TODAY (June 29, 2009). It is meant to be a bar graph of responses to the question shown in the display. a. Is response to the question a categorical or numerical variable? b. Explain why a ba

> One cause of tennis elbow, a malady that strikes fear into the hearts of all serious tennis players, is the impact induced vibration of the racket-and-arm system at ball contact. The likelihood of getting tennis elbow depends on various properties of the

> The National Center for Education Statistics included the following data on the average cost per year for tuition, fees, and room and board for four-year public institutions in the United States (nces.ed.gov/fastfacts/display.asp?id=76, retrieved April 1

> Consumer Reports (www.consumerreports.org) rated 37 different models of laptops that were for sale in 2015. An overall score was assigned to each model based on considering a number of factors, including performance, portability, and battery life. Data o

> The Census Bureau collects data on the percentage of households in the United States that have a computer. The accompanying table shows this percentage for the years 1984 to 2013 (census.gov/hhes/computer/publications/2012.html, retrieved August 1, 2016)

> The report “Credit Card & Debit Card Fraud Statistics” (www.cardhub.com/edu/credit-debit-card-fraud-statistics/, retrieved April 17, 2017) included the data in the accompanying table on the amount of money lost to

> The Census Bureau collects data on the percentage of households in the United States that have Internet access in the home. The accompanying table shows this percentage for the years 1997 to 2013 (census.gov/hhes/computer /publications/2012.html, retriev

> The accompanying table provides data on a measure of emotional health and a measure of the quality of the work environment for 12 different occupations. These data are from an article titled “U.S. Teachers Love Their Lives, but Struggle

> Data on weekday exercise time for 20 females, consistent with summary quantities given in the paper “an ecological Momentary assessment of the Physical activity and Sedentary behaviour Patterns of university Students”

> The report “Daily Cigarette Use: Indicators on Children and Youth” (Child Trends Data Bank, www .childtrends.org/wp-content/uploads/2012/11/03_Smoking _new.pdf, retrieved April 17, 2017) included the accompanying data

> Consumer Reports Health (www.consumerreports.org) gave the following data on saturated fat (in grams), sodium (in mg), and calories for 36 fast-food items. a. Construct a scatterplot using y 5 calories and x 5 fat. Does it look like there is a relations

> The accompanying data are the percentage of drivers who are uninsured in each of the 50 U.S. states and the District of Columbia (DC) as reported in the article “2015’s Most and Least Risky States for Driversâ&#1

> The accompanying frequency distribution summarizes data on the number of times smokers attempted to quit before their final successful attempt (“Demographic Variables, Smoking Variables, and Outcome Across Five Studies,â€&#15

> The accompanying data on annual maximum wind speed (in meters per second) in Hong Kong for each year in a 45-year period are from an article that appeared in the journal Renewable Energy (March 2007). Use the data to construct a histogram. Is the histogr

> The Bloomberg Visual Data web site included the following data on the total number of federal firearm background checks performed in 2014 and also the number of background checks per 1000 residents in 2014 for each of the 50 U.S. states (www.bloomberg.co

> The paper “Simpson’s Paradox: A Data and Discrimination Case Study Exercise” (Journal of Statistics Education [2014]) included data on the ages (in years) of clients of the California Department of De

> Example 2.9 provided data on seat belt use for each of the 50 U.S. states and the District of Columbia (“Traffic Safety Facts,” June, 2015, National Highway Traffic Safety Administration). The same report also gave dat

> Using the five class intervals 100 to ( 120, 120 to (140,…, 180 to , 200, construct a frequency distribution based on 70 observations whose histogram could be described as follows: a. symmetric b. bimodal c. positively skewed d. negatively skewed

> The accompanying relative frequency table is based on data from the 2015 College Bound Seniors report for California (College Board, 2016). a. Construct a relative frequency histogram for males. b. Using the same scale as the histogram from Part (a), c

> Data on weekday exercise time for 20 males, consistent with summary quantities given in the paper “an ecological Momentary assessment of the Physical activity and Sedentary behaviour Patterns of university Students” (H

> Wikipedia gives the following data on percentage increase in population between 2010 and 2015 for the 50 U.S. states and the District of Columbia (DC) (en.wikipedia.org /wiki/List_of_U.S._states_by_population_growth_rate, retrieved October 16, 2016). Eac

> Credit card fraud is a growing problem for both consumers and merchants. The data below on the percentage of credit card holders who have been impacted by fraud between 2009 and 2014 for 20 countries appeared in the article “Credit Card

> The report “Seat Belt Use in 2014” (National Highway Traffic Safety Administration) included the estimated percentages of drivers who wear seat belts for the 50 states and the District of Columbia. In the accompanying

> The following data on violent crime on Florida college campuses during 2014 are from the FBI web site. a. Construct adotplot using the 15 observations on number of violent crimes reported. Which schools stand out from the rest? b. One of the Florida sc

> An exam is given to students in an introductory statistics course. Comment on the expected shape of the histogram of scores if: a. the exam is very easy b. the exam is very difficult c. half the students in the class have had calculus, the other half

> The following two relative frequency distributions were constructed from data in the report “Undergraduate Students and Credit Cards in 2004” (Nellie Mae, May 2005). One distribution summarizes credit bureau data for a

> A report from Texas Transportation Institute (Texas A&M University System, 2005) titled “Congestion Reduction Strategies” included the following data on extra travel time during rush hour for very large and for lar

> USA TODAY (June 11, 2010) gave the following data on median age for each of the 50 U.S. states and the District of Columbia (DC). Construct a stem-and-leaf display using stems 28, 29,…,42. Comment on shape, center, and variability of

> Box Office Mojo (www.boxofficemojo.com) tracks movie ticket sales. Ticket sales (in millions of dollars) for each of the top 20 movies in 2014 and 2015 are shown in the accompanying tables. Continue to next pages… Construct com

> An article in the San Luis Obispo New Times (February 4, 2016) reported the accompanying concussion rates for different high school sports. The given data are concussion rates per 10,000 athletes participating in high school sports in 2012. a. Construct

> The 2015 urban Mobility Scorecard (texas a&M transportation institute, mobility.tamu.edu/ums/report/, rerieved april 19, 2017) included data on the estimated cost (in millions of dollars) resulting from traffic congestion for different urban areas. T

> In the United States, movies are rated by the Motion Picture Association of America (MPAA). The accompanying table gives the MPAA rating of the 25 top moneymaking movies of 2015 (data from www.boxofficemojo .com, retrieved October 10, 2016). Use the give

> The report “2013 International Bedroom Poll: Summary of Findings” describes a survey of 251 adult Americans conducted by the National Sleep Foundation (www.sleep foundation.org/sites/default/files/RPT495a.pdf, retrieved April 15, 2017). Participants in t

> The report “Findings from the 2014 College Senior Survey” (Higher Education Research Institute, December 2014) summarizes data collected from more than 13,000 college seniors across the United States. One question in t

> Heal the Bay is an environmental organization that releases an annual beach report card based on water quality (Heal the Bay Beach Report Card, www.beachreportcard.org, retrieved May 7, 2016). The grades for 20 beaches in three counties in Washington (Wh

> Each year, The Princeton Review conducts surveys of high school students who are applying to college and of parents of college applicants. The report “2016 College Hopes & Worries Survey Findings” (www.princetonre

> The report “Trends in Education 2010: Community Colleges” (www.collegeboard.com/trends) included the accompanying information on student debt for students graduating with an AA degree from a public community college in

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