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-number summary: 110 140 157 173 205. Use this information to draw a boxplot of the reading speed.
> The data in the next column represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean. (a) Draw a scatter diagram treating atmospheric pressure as the expla
> The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game. (a) A researcher wants to determine if the speed with which the ba
> The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-te
> A pediatrician wants to determine the relation that may exist between a child’s height and head circumference. She randomly selects eleven 3-year-old children from her practice, measures their heights and head circumference, and obtains the data shown in
> Your Fair Isaacs Corporation (FICO) credit score is used to determine your creditworthiness. It is used to help determine whether you qualify for a mortgage or credit and is even used to determine insurance rates. FICO scores have a range of 300 to 850,
> The Gallup Organization regularly surveys adult Americans regarding their commute time to work. In addition, they administer a Well-Being Survey. According to the Gallup Organization, “The Gallup-Healthways Well-Being Index Composite Score is comprised o
> For the 41 nations that participated in TIMMS, the correlation between the percentage of students who skipped class at least once in the past month and the mean score on the exam was -0.52. Does this suggest there is a linear relation between attendance
> Explain what is meant when we say “data vary.” How does this variability affect the results of statistical analysis?
> The Trends in International Mathematics and Science (TIMMS) is a mathematics and science achievement exam given internationally. On each exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in T
> Put the following correlation coefficients in order from weakest to strongest in terms of strength of linear association. -1, 0.377, 0.084, -0.436, 0.444, -0.733
> Put the following correlation coefficients in order from weakest to strongest in terms of strength of linear association. -0.903, 0.339, -0.431, 0.137, 0.869
> For each of the following statements, explain whether you think the variables will have positive correlation, negative correlation, or no correlation. Support your opinion. (a) Number of cigarettes smoked by a pregnant woman each week and birth weight of
> For each of the following statements, explain whether you think the variables will have positive correlation, negative correlation, or no correlation. Support your opinion. (a) Number of children in the household under the age of 3 and expenditures on di
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> The scatter diagram in the next column drawn in StatCrunch shows the relation between percent of the population with at least a bachelor’s degree in a state and birthrate (births per 1000 women 15 to 44 years old). (a) Describe any relation that exists b
> In your own words, define the four levels of measurement of a variable. Give an example of each.
> The scatter diagram drawn in Minitab shows the relation between the percentage of the population of a state plus Washington, DC, that has at least a bachelor’s degree and the median income (in dollars) of the state for 2017. Source: U.S. Census Bureau. (
> Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axes are the same for each diagram. (a) r = -0.969 (b) r = -0.049 (c) r = -1 (d) r = -0.992
> Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axes are the same for each diagram. (a) r = 0.787 (b) r = -0.787 (c) r = -0.053 (d) r = 0.946
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> True or False: Correlation implies causation.
> A _____ variable is a variable that is related to both the explanatory and response variable.
> True or False: If the linear correlation coefficient is close to 0, then the two variables have no relation.
> Contrast the differences between qualitative and quantitative variables. Discuss the differences between discrete and continuous variables.
> In a boxplot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker, the distribution is skewed________ .
> What does the five-number summary consist of?
> Explain how to determine the shape of a distribution using the boxplot and quartiles.
> 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.
> 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
> 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
> 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.
