One variable that is measured by online homework systems is the amount of time a student spends on homework for each section of the text. The following is a summary of the number of minutes a student spends for each section of the text for the fall 2018 semester in a College Algebra class at Joliet Junior College. Q1 = 42 Q2 = 51.5 Q3 = 72.5 (a) Provide an interpretation of these results. (b) Determine and interpret the interquartile range. (c) Suppose a student spent 2 hours doing homework for a section. Is this an outlier? (d) Do you believe that the distribution of time spent doing homework is skewed or symmetric? Why?
> Which boxplot shown to the right likely has the data with a larger standard deviation? Why?
> Does hunger improve strategic decision making? That is, if you are hungry are you more likely to make a favorable decision when the outcome of your decision is uncertain (as in business decisions)? To test this theory, researchers randomly divided 30 nor
> The data set “Tornadoes_2017” located at www.pearsonhighered.com/sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) Draw side-by-side boxplots of length of the tornado by month. Which mont
> Open the data 3_5_19 at www.pearsonhighered.com/sullivanstats. This data represents the amount of time of a cab ride (in seconds), the fare collected, and the payment method for a random sample of 100 rides in the City of Chicago. Source: Chicago Data Po
> It is well- documented that active maternal smoking during pregnancy is associated with lower-birth-weight babies. Researchers wanted to determine if there is a relationship between paternal smoking habits and birth weight. The researchers administered
> In April, 2014, the city of Flint, Michigan stopped buying water that came from Lake Huron and started using water from the Flint River to save money. After the move, residents of Flint started experiencing symptoms that could be attributed to the consum
> Do store-brand chocolate chip cookies have fewer chips per cookie than Keebler’s Chips Deluxe Chocolate Chip Cookies? To find out, a student randomly selected 21 cookies of each brand and counted the number of chips in the cookies. The results are shown
> Explain the difference between a population and a sample.
> Ty Cobb is one of Major League Baseball’s greatest hitters of all time, with a career batting average of 0.366. Source: baseball-almanac.com
> A student wanted to know whether Centrum vitamins dissolve faster than the corresponding generic brand. The student used vinegar as a proxy for stomach acid and measured the time (in minutes) it took for a vitamin to completely dissolve. The results are
> In Problem 26 from Section 3.1, we drew a histogram of the length of eruption of California’s Old Faithful geyser and found that the distribution is symmetric. Draw a boxplot of these data. Use the boxplot and quartiles to confirm the distribution is s
> In Problem 25 from Section 3.1, we drew a histogram of the weights of M&Ms and found that the distribution is symmetric. Draw a boxplot of these data. Use the boxplot and quartiles to confirm the distribution is symmetric. For convenience, the data are d
> The following data represent the weight (in grams) of a random sample of 25 Tylenol tablets. (a) Construct a boxplot. (b) Use the boxplot and quartiles to describe the shape of the distribution.
> The data below represent the age of the mother at the time of her first birth for a random sample of 30 mothers. (a) Construct a boxplot of the data. (b) Use the boxplot and quartiles to describe the shape of the distribution.
> The following data represent the percentage of workers who carpool to work for the 50 states plus Washington, D.C. Note: The minimum observation of 7.2% corresponds to Maine and the maximum observation of 16.4% corresponds to Hawaii. (a) Find the five-nu
> The following data represent the age of U.S. presidents on their respective inauguration days (through Donald Trump). (a) Find the five-number summary. (b) Construct a boxplot. (c) Comment on the shape of the distribution.
> Jessica enrolled in a course that promised to increase her reading speed. To help judge the effectiveness of the course, Jessica measured the number of words per minute she could read prior to enrolling in the course. She obtained the following five-numb
> After giving a statistics exam, Professor Dang determined the following five-number summary for her class results: 60 68 77 89 98. Use this information to draw a boxplot of the exam scores.
> Use the side-by-side boxplots shown to answer the questions that follow. (a) To the nearest integer, what is the median of variable x? (b) To the nearest integer, what is the first quartile of variable y? (c) Which variable has more dispersion? Why? (d)
> Read the newspaper article and answer the following questions: (a) What is the research question the study addresses? (b) What is the sample? (c) What type of variable is season in which you were born? (d) What can be said (in general) about individuals
> Use the side-by-side boxplots shown to answer the questions that follow. (a) To the nearest integer, what is the median of variable x? (b) To the nearest integer, what is the third quartile of variable y? (c) Which variable has more dispersion? Why? (d)
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> ______ divide data sets into fourths.
> The_______ of a data set is a value such that k percent of the observations are less than or equal to the value.
> The_______ represents the number of standard deviations an observation is from the mean.
> Explain what each quartile represents.
> Explain the circumstances for which the interquartile range is the preferred measure of dispersion. What is an advantage that the standard deviation has over the interquartile range?
> Explain the advantage of using z-scores to compare observations from two different data sets.
> Mensa is an organization designed for people of high intelligence. One qualifies for Mensa if one’s intelligence is measured at or above the 98th percentile. Explain what this means.
> Suppose a fundraiser holds a raffle for which each person who enters the room receives a ticket numbered 1 to N, where N is the number of people at the fundraiser. The first person to arrive receives ticket number 1, the second person receives ticket num
> When outliers are discovered, should they always be removed from the data set before further analysis?
> Morningstar is a mutual fund rating agency. It ranks a fund’s performance by using one to five stars. A one-star mutual fund is in the bottom 10% of its investment class; a five-star mutual fund is at the 90th percentile of its investment class. Interpre
> Suppose you received the highest score on an exam. Your friend scored the second-highest score, yet you both were in the 99th percentile. How can this be?
> Write a paragraph that explains the meaning of percentiles.
> Use the fraud-detection data from Problem 25 to do the following. (a) Determine the standard deviation and interquartile range of the data. (b) Suppose the month in which the customer used 346 minutes was not actually that customer’s phone. That particul
> Use the results of Problem 22 in Section 3.1 and Problem 22 in Section 3.2 to compute the z-scores for all the students. Compute the mean and standard deviation of these z-scores.
> The data set “Tornadoes_2017” located at www.pearsonhighered.com/sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) Determine and interpret the quartiles of the length for all tornadoes. (
> A survey of 40 randomly selected full-time Joliet Junior College students was conducted in the Fall 2019 semester. In the survey, the students were asked to disclose their weekly spending on entertainment. The results of the survey are as follows: (a) Ch
> A survey of 50 randomly selected full-time Joliet Junior College students was conducted during the Fall 2019 semester. In the survey, the students were asked to disclose their weekly income from employment. If the student did not work, $0 was entered. (a
> A credit card company has a fraud- detection service that determines if a card has any unusual activity. The company maintains a database of daily charges on a customer’s credit card. Days when the card was inactive are excluded from the database. If a d
> It is extremely important for a researcher to clearly define the variables in a study because this helps to determine the type of analysis that can be performed on the data. For example, if a researcher wanted to describe baseball players based on jersey
> As part of its “Customers First” program, a cellular phone company monitors monthly phone usage. The program identifies unusual use and alerts the customer that their phone may have been used by another person. The data represent the monthly phone use in
> The following data represent the number of days between grocery orders at the online delivery company Instacart. (a) Determine and interpret the quartiles. (b) Check the data set for outliers.
> The following data represent the wait time (in minutes) for a random sample of 40 visitors to Disney’s Dinosaur Ride in Animal Kingdom. (a) Determine and interpret the quartiles. (b) Check the data set for outliers.
> The following data represent the hemoglobin (in g/dL) for 20 randomly selected cats. (a) Compute the z-score corresponding to the hemoglobin of Blackie, 7.8 g/dL. Interpret this result. (b) Determine the quartiles. (c) Compute and interpret the interquar
> The following data represent the miles per gallon of a random sample of SMART cars with a three-cylinder, 1.0-liter engine. (a) Compute the z-score corresponding to the individual who obtained 36.3 miles per gallon. Interpret this result. (b) Determine t
> The following graph is an ogive of the mathematics scores on the SAT. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile. (a) Find and interpret the percentile rank of a student who scored 400 o
> The following graph is an ogive of IQ scores. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile. (a) Find and interpret the percentile rank of an individual whose IQ is 100. (b) Find and interp
> Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all 50 states in the United States plus Washington, D.C., in 2017. Q1 = 244.8 Q2 = 357.6 Q3 =
> Explain the meaning of the following percentiles. Source: National Center for Health Statistics. (a) The 5th percentile of the weight of males 36 months of age is 12.0 kg. (b) The 95th percentile of the length of newborn females is 53.8 cm.
> The data set “Tornadoes_2017” located at www.pearsonhighered.com/ sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. For each of the following variables in the data set, indicate the level of
> Explain the meaning of the following percentiles. Source: Advance Data from Vital and Health Statistics. (a) The 15th percentile of the head circumference of males 3 to 5 months of age is 41.0 cm. (b) The 90th percentile of the waist circumference of fem
> A manufacturer of bolts has a quality- control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The quality-control engineer knows that the bolts coming off the assembly line have a mean length of 8 cm
> A highly selective boarding school will only admit students who place at least 1.5 standard deviations above the mean on a standardized test that has a mean of 200 and a standard deviation of 26. What is the minimum score that an applicant must make on t
> Roberto finishes a triathlon (750-meter swim, 5-kilometer run, and 20-kilometer bicycle) in 63.2 minutes. Among all men in the race, the mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. Zandra finishes the same triathlon in
> Ryan Murphy, nephew of the author, swims for U.S.A. Swimming. While he was in college at the University of California at Berkeley, Ryan’s best time in the 100-meter backstroke was 45.3 seconds. The mean of all NCAA swimmers in this event is 48.62 seconds
> The highest batting average ever recorded in Major League Baseball was by Ted Williams in 1941 when he hit 0.406. That year, the mean and standard deviation for batting average were 0.2806 and 0.0328. In 2018, Mookie Betts was the American League batting
> In 2018, Jacob deGrom of the New York Mets had the lowest earned-run average (ERA is the mean number of runs yielded per nine innings pitched) of any starting pitcher in the National League, with an ERA of 1.70. Also in 2018, Blake Snell of the Tampa Bay
> The average 20- to 29-year-old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while the average 20- to 29-year-old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 67-inch man or a 62-inch
> The average 20- to 29-year-old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while the average 20- to 29-year-old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 75-inch man or a 70-inch
> Babies born after a gestation period of 32–35 weeks have a mean weight of 2600 grams and a standard deviation of 660 grams. Babies born after a gestation period of 40 weeks have a mean weight of 3500 grams and a standard deviation of 470 grams. Suppose a
> The data set “Tornadoes_2017” located at www.pearsonhighered.com/ sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. For each of the following variables in the data set, indicate whether the v
> Babies born after a gestation period of 32–35 weeks have a mean weight of 2600 grams and a standard deviation of 660 grams. Babies born after a gestation period of 40 weeks have a mean weight of 3500 grams and a standard deviation of 470 grams. Suppose a
> The_______ is the range of the middle 50% of the observations in a data set.
> Often, frequency distributions are reported using unequal class widths because the frequencies of some groups would otherwise be small or very large. Consider the following data, which represent the daytime household temperature the thermostat is set to
> The frequency distribution below represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.
> Recently, a random sample of 25–34 year olds was asked, “How much do you currently have in savings, not including retirement savings?” The following data represent the responses to the survey. Approximate the mean and standard deviation amount of savings
> Determine the modal class of the frequency distribution in Problem 2.
> Determine the modal class of the frequency distribution in Problem 1.
> Approximate the median of the frequency distribution in Problem 4.
> Approximate the median of the frequency distribution in Problem 2.
> The following data represent the age of the mother at childbirth for 1980 and 2017. (a) Approximate the population mean and standard deviation of age for mothers in 1980. (b) Approximate the population mean and standard deviation of age for mothers in 20
> The Gallup Organization conducted a survey of 1018 adults, aged 18 and older, living in the United States and asked, “If you had a thousand dollars to spend, do you think investing it in the stock market would be a good or bad idea?” Of the 1018 adults,
> The data represent the male and female population, by age, of the United States in 2017. Note: Use 85 for the class midpoint of Ú 80. (a) Approximate the population mean and standard deviation of age for males. (b) Approximate the population mean and sta
> Michael and Kevin return to the candy store, but this time they want to purchase nuts. They can’t decide among peanuts, cashews, or almonds. They again agree to create a mix. They bought 2.5 pounds of peanuts for $1.30 per pound, 4 pounds of cashews for
> Michael and Kevin want to buy chocolates. They can’t agree on whether they want chocolate- covered almonds, chocolate-covered peanuts, or chocolate- covered raisins. They agree to create a mix. They bought 4 pounds of chocolate-covered almonds at $3.50 p
> In Marissa’s calculus course, attendance counts for 5% of the grade, quizzes count for 10% of the grade, exams count for 60% of the grade, and the final exam counts for 25% of the grade. Marissa had a 100% average for attendance, 93% for quizzes, 86% for
> Marissa has just completed her second semester in college. She earned a B in her five-hour calculus course, an A in her three-hour social work course, an A in her four-hour biology course, and a C in her three-hour American literature course. Assuming th
> Use the frequency distribution whose class width is 0.5 obtained in Problem 30 in Section 2.2 to approximate the mean and standard deviation for cigarette tax rates. Compare these results to the actual mean and standard deviation.
> Use the frequency distribution whose class width is 4 obtained in Problem 29 in Section 2.2 to approximate the mean and standard deviation exit velocity. Compare these results to the actual mean and standard deviation exit velocity.
> The following frequency distribution represents the birth weight of all babies born in the United States in 2017. (a) Approximate the mean and standard deviation birth weight. (b) Draw a frequency histogram of the data to verify that the distribution is
> The following data represent the number of live multiple-delivery births (three or more babies) in 2017 for women 15 to 54 years old. (a) Approximate the mean and standard deviation for age. (b) Draw a frequency histogram of the data to verify that the d
> The following frequency distribution represents the age of people living in poverty in 2018 based on a random sample of residents of the United States. In this frequency distribution, the class widths are not the same for each class. Approximate the mean
> Gallup News Service conducted a survey of 1017 American adults aged 18 years or older. The respondents were asked, “Of every tax dollar that goes to the federal government in Washington, D.C., do you believe 51 cents or more are wasted?” Of the 1017 indi
> The sum of the deviations about the mean always equals_____ .
> In 2000, the Walt Disney Company created the “fast pass” —a ticket issued to a rider for a popular ride and the rider is told to return at a specific time during the day. At that time, the rider is allowed to bypass the regular line, thereby reducing the
> Draw two histograms with different standard deviations and label them I and II. Which histogram has the larger standard deviation?
> Develop a sample of size n = 8 such that /and s = 0.
> Which of the following would have a higher standard deviation? (a) IQ of students on your campus or (b) IQ of residents in your home town? Why?
> Explain how standard deviation measures spread. In your explanation include the computation of the same standard deviation for two data sets: Data set I: 3, 4, 5; Data set II: 0, 4, 8.
> In one of Sullivan’s statistics sections, the standard deviation of the heights of all students was 3.9 inches. The standard deviation of the heights of males was 3.4 inches and the standard deviation of females was 3.3 inches. Why is the standard deviat
> What makes the range less desirable than the standard deviation as a measure of dispersion?
> What does it mean when a statistic is biased?
> Are any of the measures of dispersion mentioned in this section resistant? Explain.
> A study was designed “to determine if application of duct tape is as effective as cryotherapy (liquid nitrogen applied to the wart for 10 seconds every 2 to 3 weeks) in the treatment of common warts.” The researchers randomly divided 51 patients into two
> What is meant by the phrase degrees of freedom as it pertains to the computation of the sample standard deviation?
> Would it be appropriate to say that a distribution with a standard deviation of 10 centimeters is more dispersed than a distribution with a standard deviation of 5 inches? Support your position.
> The data set “Tornadoes_2017” located at www.pearsonhighered.com/ sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) Determine the range and standard deviation of the length for all tornad
> Survey Choose any quantitative variable from the SullivanStatsSurveyI at www.pearsonhighered.com/sullivanstats. Now choose a qualitative variable, such as gender or political philosophy. Determine the range and standard deviation by the qualitative varia
