Population: 1, 19, 25, 15, 12, 16, 28, 13, 6
> 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
> Choose two quantitative variables from the SullivanStatsSurveyI at www.pearsonhighered.com/sullivanstats for which a comparison is reasonable, such as number of hours of television versus number of hours of Internet. Draw a histogram for each variable. W
> The data set on the left represents the annual rate of return (in percent) of eight randomly sampled bond mutual funds, and the data set on the right represents the annual rate of return (in percent) of eight randomly sampled stock mutual funds. (a) Dete
> A popular theory in investment states that you should invest a certain amount of money in foreign investments to reduce your risk. The risk of a portfolio is defined as the standard deviation of the rate of return. Refer to the graph, which depicts the r
> Karl Pearson developed a measure that describes the skewness of a distribution, called the coefficient of skewness. The formula is The value of this measure generally lies between -3 and +3. The closer the value lies to -3, the more the distribution is s
> Another measure of variation is the mean absolute deviation. It is computed using the formula Compute the mean absolute deviation of the data in Problem 11 and compare the results with the sample standard deviation.
> Blocking refers to the idea that we can reduce the variability in a variable by segmenting the data by some other variable. The given data represent the recumbent length (in centimeters) of a sample of 10 males and 10 females who are 40 months of age. (a
> A study was conducted in which 20,211 18-year- old Israeli male military recruits were given an exam to measure IQ. In addition, the recruits were asked to disclose their smoking status. An individual was considered a smoker if he smoked at least one cig
> The following data represent the asking price, in dollars, for a random sample of 2014 coupes (a two-door car) and a random sample of 2014 Chevy Camaros. (a) Find the mean and standard deviation price for each sample. (b) Explain why the mean is higher f
> Compute the sample standard deviation of the following test scores: 78, 78, 78, 78. What can be said about a data set in which all the values are identical?
> Each of the following three data sets represents the IQ scores of a random sample of adults. IQ scores are known to have a mean and median of 100. For each data set, determine the sample standard deviation. Then recompute the sample standard deviation as
> Benjamin owns a small Internet business. Besides himself, he employs nine other people. The salaries earned by the employees are given next in thousands of dollars (Benjamin’s salary is the largest, of course): 30, 30, 45, 50, 50, 50, 55, 55, 60, 75 (a)
> The standard deviation of batting averages of all teams in the American League is 0.008. The standard deviation of all players in the American League is 0.02154. Why is there less variability in team batting averages?
> According to the U.S. Census Bureau, the mean of the commute time to work for a resident of Boston, Massachusetts, is 27.3 minutes. Assume that the standard deviation of the commute time is 8.1 minutes to answer the following: (a) What minimum percentage
> In December 2018, the average price of regular unleaded gasoline excluding taxes in the United States was $3.06 per gallon, according to the Energy Information Administration. Assume that the standard deviation price per gallon is $0.06 per gallon to ans
> Lawrence Summers (former Secretary of the Treasury and former president of Harvard) infamously claimed that women have a lower standard deviation IQ than men. He went on to suggest that this was a potential explanation as to why there are fewer women in
> Suppose Professor Alpha and Professor Omega each teach Introductory Biology. You need to decide which professor to take the class from and have just completed your Introductory Statistics course. Records obtained from past students indicate that students
> The distribution of the length of bolts has a bell shape with a mean of 4 inches and a standard deviation of 0.007 inch. (a) About 68% of bolts manufactured will be between what lengths? (b) What percentage of bolts will be between 3.986 inches and 4.014
> The following information relates to the 2019 model year product line of BMW automobiles.
> In a national survey on substance abuse, 13.3% of 12th graders reported using illicit drugs within the past month. Source: National Institute on Drug Abuse
> The weight, in grams, of the pair of kidneys in adult males between the ages of 40 and 49 has a bell- shaped distribution with a mean of 325 grams and a standard deviation of 30 grams. (a) About 95% of kidney pairs will be between what weights? (b) What
> SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114. Source: College Board. (a) What percentage of SAT scores is between 401 and 629? (b) What percentage of SAT scores is less than 401 or greater than 629? (
> The Stanford—Binet Intelligence Quotient (IQ) measures intelligence. IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. (a) What percentage of people has an IQ score between 70 and 130? (b) What percentage of peo
> It is well known that San Diego has milder weather than Chicago, but which city has more deviation from normal temperatures? Use the following data, which represent the deviation from normal high temperatures for a random sample of days. In which city wo
> Stocks may be categorized by sectors. Go to www.pearsonhighered.com/sullivanstats and download 3_2_29 using the file format of your choice. The data represent the one-year rate of return (in percent) for a sample of consumer cyclical stocks and industria
> You have received a year-end bonus of $5000. You decide to invest the money in the stock market and have narrowed your investment options down to two mutual funds. The following data represent the historical quarterly rates of return of each mutual fund
> Suppose that you are in the market to purchase a car. You have narrowed it down to two choices and will let gas mileage be the deciding factor. You decide to conduct a little experiment in which you put 10 gallons of gas in the car and drive it on a clos
> The following data represent the length of eruption for a random sample of eruptions at the Old Faithful geyser in Calistoga, California. (a) Determine the sample standard deviation length of eruption. Express your answer rounded to the nearest whole num
> The following data represent the weights (in grams) of a random sample of 50 M&M plain candies. (a) Determine the sample standard deviation weight. Express your answer rounded to three decimal places. (b) On the basis of the histogram drawn in Section 3.
> The data below represent the number of pods on a sample of soybean plants for two different plot types. Which plot type do you think is superior? Why?
> The following data represent driver’s license laws for various states.
> Ethan and Drew went on a 10-day fishing trip. The number of smallmouth bass caught and released by the two boys each day was as follows: (a) Find the population mean and the range for the number of smallmouth bass caught per day by each fisherman. Do the
> The following data represent the travel time (in minutes) to school for nine students enrolled in Sullivan’s College Algebra course. Treat the nine students as a population. (a) Determine the population standard deviation. (b) Find three simple random sa
> The data represent the pulse rates (beats per minute) of nine students enrolled in a section of Sullivan’s course in Introductory Statistics. Treat the nine students as a population. (a) Determine the population standard deviation. (b) Find three simple
> The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic, while a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water. (a) Which type of water has more dispersion in
> The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a “flipped” classroom. The “flipped” classroom is one where the content is delivered via video and watched at home, while class time
> (a) Suppose in a certain set of data, there are two observations of 90 and 100. Is 90 far away from 100 if the standard deviation of the data is 10? (b) Suppose in a certain set of data, there are two observations of 90 and 100. Is 90 far away from 100 i
> For each of the following data sets, decide which has the higher standard deviation (set 1 or set 2), if any, without doing any computation. Explain the rationale behind your choice. Then, verify your choice by computing the standard deviation by hand.
> Match the histograms in the next column to the summary statistics given.
> Which histogram depicts a higher standard deviation? Justify your answer.
> The following data represent the flight time (in minutes) of a random sample of seven flights from Las Vegas, Nevada, to Newark, New Jersey, on United Airlines. Compute the range and sample standard deviation of flight time. 282, 270, 260, 266, 257, 260,
> A community college notices that an increasing number of full-time students are working while attending the school. The administration randomly selects 128 students and asks how many hours per week each works.
> A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The strength of concrete is measured by pouring the mix into casting cylinders after it is allowed to set up for 28 days. The following data represent
> The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in Sullivan’s Statistics course. Compute the range, sample variance, and sample standard deviation time. 60.5, 1
> The following data represent the miles per gallon for a 2013 Ford Fusion for six randomly selected vehicles. Compute the range, sample variance, and sample standard deviation miles per gallon. Source: www.fueleconomy.gov 34.0, 33.2, 37.0, 29.4, 23.6, 25.
> Population: 4, 10, 12, 12, 13, 21
> Sample: 6, 52, 13, 49, 35, 25, 31, 29, 31, 29
> Population: 3, 6, 10, 12, 14
> Sample: 83, 65, 91, 87, 84
> Sample: 20, 13, 4, 8, 10
> True or False: Chebyshev’s Inequality applies to all distributions regardless of shape, but the Empirical Rule holds only for distributions that are bell shaped
> Researchers want to determine whether or not higher folate intake is associated with a lower risk of hypertension (high blood pressure) in women (27 to 44 years of age). To make this determination, they look at 7373 cases of hypertension in these women a
> True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure.
> The standard deviation is used in conjunction with the____ to numerically describe distributions that are bell shaped. The_____ measures the center of the distribution, while the standard deviation measures the ______of the distribution.
> True or False: A data set will always have exactly one mode.
> If a data set contains 10,000 values arranged in increasing order, where is the median located?
> A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why?
> The U.S. Department of Housing and Urban Development (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the median?
> The Federal Reserve Bank of St. Louis reported two average personal incomes for 2018: $33,706 and $50,731. One of these averages is the mean and the other is the median. Which is the mean? Support your answer.
> What does it mean if a statistic is resistant?
> For each of the following situations, determine which measure of central tendency is most appropriate and justify your reasoning. (a) Average price of a home sold in Pittsburgh, Pennsylvania, in 2019 (b) Most popular major for students enrolled in a stat
> In January 2020, the mean amount of money lost per visitor to a local riverboat casino was $135. Do you think the median was more than, less than, or equal to this amount? Why?
> Every year the U.S. Census Bureau releases the Current Population Report based on a survey of 50,000 households. The goal of this report is to learn the demographic characteristics, such as income, of all households within the United States.
> You are negotiating a contract for the Players Association of the NBA. Which measure of central tendency will you use to support your claim that the average player’s salary needs to be increased? Why? As the chief negotiator for the owners, which measure
> According to MarketWatch, the mean net worth of all individuals in the United States in 2016 was $692,100, while the median net worth was $97,300. (a) Which measure do you believe better describes the typical individual’s net worth? Support your opinion.
> A researcher with the Department of Energy wants to determine the mean natural gas bill of households throughout the United States. He knows the mean natural gas bill of households for each state, so he adds together these 50 values and divides by 50 to
> Why is the median resistant, but the mean is not?
> The Fair Isaacs Corporation has devised a model that is used to determine creditworthiness of individuals, called a FICO score. FICO scores range in value from 300 to 850, with a higher score indicating a more creditworthy individual. The distribution of
> As part of a semester project in a statistics course, Carlos surveyed a sample of 50 high school students and asked, “How many days in the past week have you consumed an alcoholic beverage?” The results of the survey are shown next. (a) Is this data disc
> 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 mean and median length for all tornadoes. What shape would
> The midrange is also a measure of central tendency. It is computed by adding the smallest and largest observed values of a data set and dividing the result by 2; that is, Compute the midrange for the data in Problem 25. Is the midrange resistant? Explain
> Another measure of central tendency is the trimmed mean. It is computed by determining the mean of a data set after deleting the smallest and largest observed values. Compute the trimmed mean for the data in Problem 25. Is the trimmed mean resistant? Exp
> Use the five test scores of 65, 70, 71, 75, and 95 to answer the following questions: (a) Find the sample mean. (b) Find the median. (c) Which measure of central tendency better describes the typical test score? (d) Suppose the professor decides to curve
> A farmer interested in the weight of his soybean crop randomly samples 100 plants and weighs the soybeans on each plant.
> Benjamin owns a small Internet business. Besides himself, he employs nine other people. The salaries earned by the employees are given next in thousands of dollars (Benjamin’s salary is the largest, of course): 30, 30, 45, 50, 50, 50, 55, 55, 60, 75 (a)
> Go to http://www.pearsonhighered.com/ sullivanstats and download the SullivanStatsSurvey I data. The data represent the results of a survey conducted by the author. The column “Texts” represents the number of texts the individual sent for the month prior
> Go to http://www.pearsonhighered.com/sullivanstats to obtain the data 3_1_35. The data represent the blood alcohol concentration (BAC), in percent, of a random sample of drivers involved in fatal car accidents. A BAC of 0 indicates that no alcohol was pr
> Unfortunately, a friend of yours has been diagnosed with cancer. A histogram of the survival time (in months) of patients diagnosed with this form of cancer is shown in the figure; the median survival time is 11 months, while the mean survival time is 69
> A professor has recorded exam grades for 20 students in his class, but one of the grades is no longer readable. If the mean score on the exam was 82 and the mean of the 19 readable scores is 84, what is the value of the unreadable score?
> Mr. Zuro finds the mean height of all 14 students in his statistics class to be 68.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 65 inches tall. What is the mean height of the 15 students in the c
> Each of the following three data sets in the next column represents the IQ scores of a random sample of adults. IQ scores are known to have a mean and median of 100. For each data set, determine the mean and median. For each data set recalculate the mean
> The following data represent the diagnosis of a random sample of 20 patients admitted to a hospital. Determine the mode diagnosis.
> A sample of 30 registered voters was surveyed in which the respondents were asked, “Do you consider your political views to be conservative, moderate, or liberal?” The results of the survey are shown in the table. (a) Determine the mode political view. (
> The following data represent the number of days between grocery orders at the online delivery company Instacart. Determine the shape of the distribution of days between orders by drawing a frequency histogram. Find the mean and median days between orders
> A quality-control manager randomly selects 50 bottles of Coca-Cola that were filled on October 15 to assess the calibration of the filling machine.
> The following data represent the wait time (in minutes) for a random sample of 40 visitors to Disney’s Dinosaur Ride in Animal Kingdom. Determine the shape of the distribution of wait time by drawing a frequency histogram. Find the mean and median wait t
> We have all heard of the Old Faithful geyser in Yellowstone National Park. However, there is another, less famous, Old Faithful geyser in Calistoga, California. The following data represent the length of eruption (in seconds) for a random sample of erupt
> The following data represent the weights (in grams) of a simple random sample of 50 M&M plain candies. Determine the shape of the distribution of weights of M&Ms by drawing a frequency histogram. Find the mean and median. Which measure of central tendenc
> A histogram of the annual subscription cost (in dollars) for 26 biology journals is shown. The mean subscription cost is $1846 and the median subscription cost is $1142. Identify the shape of the distribution. Which measure of central tendency better des
> A histogram of the download time of a movie, in minutes, for 30 randomly selected movies is shown. The mean download time is 39.007 minutes and the median download time is 39.065 minutes. Identify the shape of the distribution. Which measure of central t
> The data on the next page represent the travel time (in minutes) to school for nine students enrolled in Sullivan’s College Algebra course. Treat the nine students as a population. (a) Determine the population mean travel time. (b) Find three simple rand
> The following data represent the pulse rates (beats per minute) of nine students enrolled in a section of Sullivan’s Introductory Statistics course. Treat the nine students as a population. (a) Determine the population mean pulse. (b) Find three simple r
> The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water. (a) Determine the mean, median, and mode pH for each
> The data in the next column represent exam scores in a statistics class taught using traditional lecture and a class taught using a “flipped” classroom. The “flipped” classroom is one where the content is delivered via video and watched at home, while cl
> Match the histograms shown to the summary statistics:
> The Gallup Organization contacts 1028 teenagers who are 13 to 17 years of age and live in the United States and asks whether or not they had been prescribed medications for any mental disorders, such as depression or anxiety.
> For each of the three histograms shown, determine whether the mean is greater than, less than, or approximately equal to the median. Justify your answer.
> The following data represent the flight time (in minutes) of a random sample of seven flights from Las Vegas, Nevada, to Newark, New Jersey, on United Airlines. Compute the mean, median, and mode flight time. 282, 270, 260, 266, 257, 260, 267
