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mathematics
statistics the art and science

Questions and Answers of Statistics The Art and Science

The value 88 in a dataset with mean 96 and standard deviation 10.Find and interpret the z-score for the data value given.
The value 5.2 in a dataset with mean 12 and standard deviation 2.3.Find and interpret the z-score for the data value given.
The value 8.1 in a dataset with mean 5 and standard deviation 2.Find and interpret the z-score for the data value given.
Abell-shaped distribution with mean 200 and standard deviation 25.The 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval
A bell-shaped distribution with mean 10 and standard deviation 3.The 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval
A bell-shaped distribution with mean 1000 and standard deviation 10.The 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an
A bell-shaped distribution with mean 1500 and standard deviation 300.The 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an
Computer output giving descriptive statistics for the percent of the population that is obese for each of the 50 US states, from the USStates dataset, is given in Figure 2.27. Since all 50 US states
Computer output giving descriptive statistics for the percent of the population that is obese for each of the 50 US states, from the USStates dataset, is given in Figure 2.27.Figure 2.27(a) What is
Every Fourth of July, Nathan’s Famous in New York City holds a hot dog eating contest in which contestants try to eat as many hot dogs as possible in 10 minutes. In 2011, over 30,000 people watched
In Exercise 2.98, we mention that either Joey Chestnut of California, US, or Takeru Kobayashi of Japan has won the Nathan€™s Famous Hot Dog Eating Contest every year from 2002 until 2011.
Studies have shown that heating the scrotum by just 1◦C can reduce sperm count and sperm quality, so men concerned about fertility are cautioned to avoid too much time in the hot tub or sauna. A
Exercise 1.20 on page 15 gives a sample of eight times, in days, to row solo across the Atlantic Ocean. The times are(a) Use technology to find the mean and standard deviation of the eight times.(b)
A histogram of the n = 345 grade point averages reported by students in the Student Survey dataset is shown in Figure 2.28.(a) Estimate and interpret the 10th percentile and the 75th
Exercise 2.51 on page 71 discusses the use of toenail clippings to measure the level of arsenic exposure of individuals in Great Britain. A similar study was conducted in the US. Table 2.23 gives
Figure 2.29 shows a dotplot of the arsenic concentrations in Table 2.23.Figure 2.29Table 2.23(a) Which measures of center and spread are most appropriate for this distribution: the mean and standard
In basketball, a basket is awarded three points (rather than the usual two) if it is shot from farther away. Some players attempt lots of three-point shots and quite a few attempt none, as we see in
The variable Blocks in the dataset NBA Players 2011 includes information on the number of blocked shots during the season for each of the 176 players in the dataset.(a) Use technology to find the
Table 2.24 shows the means and standard deviations for four of the variables in the NBAPlayers2011 dataset. FGPct is the field goal percentage, Points is total number of points scored during the
Stanley, a recent high school student, took the SAT exam in 2011 and got a 600 in all three components (Critical Reading, Math, and Writing). He was interested in how well he did compared to the rest
The Nielsen Company measured connection speeds on home computers in nine different countries and wanted to determine whether connection speed affects the amount of time consumers spend online. Table
Consider the jogging times from a set of 5-mile runs by two different runners in Table 2.27.Jogger 1......................................Jogger
Table 2.14 on page 61 shows longevity (typical lifespan) in years for 40 species of mammals, and the data are also available in MammalLongevity.Table 2.14(a) Use technology to find the mean and
The five number summary for daily calorie consumption for the n = 315 participants in the NutritionStudy is (445, 1334, 1667, 2106, 6662).(a) Give the range and the IQR.(b) Which of the following
Using only the whole numbers 1 through 9 as possible data values, create a dataset with n = 6 and x̅ = 5 and with:(a) Standard deviation as small as possible.(b) Standard deviation as large as
Mean 7 and standard deviation 1.Sketch a curve showing a distribution that is symmetric and bell-shaped and has approximately the given mean and standard deviation. In each case, draw the curve on a
Mean 5 and standard deviation 2.Sketch a curve showing a distribution that is symmetric and bell-shaped and has approximately the given mean and standard deviation. In each case, draw the curve on a
Mean 5 and standard deviation 0.5.Sketch a curve showing a distribution that is symmetric and bell-shaped and has approximately the given mean and standard deviation. In each case, draw the curve on
Draw a histogram or a smooth curve illustrating the shape of a distribution with the properties that:(a) The range is 100 and the interquartile range is 10(b) The range is 50 and the interquartile
According to the 95% rule, the largest value in a sample from a distribution which is approximately symmetric and bell-shaped should be between 2 and 3 standard deviations above the mean, while the
Match each five number summary with one of the boxplots inFigure 2.37.(a) (2, 12, 14, 17, 25)(b) (5, 15, 18, 20, 23)(c) (10, 12, 13, 18, 25)(d) (12, 12, 15, 20, 24)Match the five number summaries
Show a boxplot for a set of data. In each case:(a) Indicate whether the distribution of the data appears to be skewed to the left, skewed to the right, approximately symmetric, or none of these.(b)
Show a boxplot for a set of data. In each case:(a) Indicate whether the distribution of the data appears to be skewed to the left, skewed to the right, approximately symmetric, or none of these.(b)
Show a boxplot for a set of data. In each case:(a) Indicate whether the distribution of the data appears to be skewed to the left, skewed to the right, approximately symmetric, or none of these.(b)
Show a boxplot for a set of data. In each case:(a) Indicate whether the distribution of the data appears to be skewed to the left, skewed to the right, approximately symmetric, or none of these.(b)
The variables in USStates include the percent of the people in each state who say they have engaged in any physical activity in the last month as well as the region of the country in which the state
Five number summary: (210, 260, 270, 300, 320); n = 500Tails: 210, 215, 217, 221, 225, . . ., 318, 319, 319, 319, 320, 320Each describe a sample. The information given includes the five number
Five number summary: (15, 42, 52, 56, 71); n = 120Tails: 15, 20, 28, 30, 31, . . ., 64, 65, 65, 66, 71Each describe a sample. The information given includes the five number summary, the sample size,
Five number summary: (42, 72, 78, 80, 99); n = 120Tails: 42, 63, 65, 67, 68, . . ., 88, 89, 95, 96, 99Each describe a sample. The information given includes the five number summary, the sample size,
Five number summary: (5, 10, 12, 16, 30); n = 40Tails: 5, 5, 6, 6, 6, . . ., 22, 22, 23, 28, 30Each describe a sample. The information given includes the five number summary, the sample size, and the
The dataset Hollywood- Movies2011 includes a quantitative variable on the AudienceScore of the movie as well as a categorical variable classifying each movie by its Genre. The computer output below
One of the variables in the HollywoodMovies2011 dataset is Profitability, which measures the proportion of the budget recovered in revenue from the movie. A profitability less than 1 means the movie
Audience scores (on a scale from 1 to 100) on the Rotten Tomatoes website for all movies that came out of Hollywood in 2011 have a five number summary of (24, 49, 61, 77, 93). (These data are in the
The dataset HollywoodMovies2011 includes a quantitative variable on the Budget of the movie, in millions of dollars, as well as a categorical variable classifying each movie by its Genre. Figure 2.40
Estimate the five number summary for the data in Figure 2.26.Estimate the summary statistics requested, using the histogram in Figure 2.26. There are n = 100 data points included in the
Estimate values at the 10th percentile and the 90th percentile for the data in Figure 2.26.Estimate the summary statistics requested, using the histogram in Figure 2.26. There are n = 100 data points
Estimate the mean and the standard deviation for the data in the dotplot in Figure 2.26.Estimate the summary statistics requested, using the histogram in Figure 2.26. There are n = 100 data points
Estimate the five number summary for the data in Figure 2.25.Estimate the summary statistics requested, using the histogram in Figure 2.25. There are n = 100 data points included in the
Estimate values at the 10th percentile and the 90th percentile for the data in Figure 2.25.Estimate the summary statistics requested, using the histogram in Figure 2.25. There are n = 100 data points
Match each five number summary with one of the histograms in Figure 2.24. The scale is the same on all four histograms.(a) (1, 3, 5, 7, 9)(b) (1, 4, 5, 6, 9)(c) (1, 5, 7, 8, 9)(d) (1, 1, 2, 4,
Match each five number summary with one of the histograms inFigure 2.23.(a) (0, 0.25, 0.5, 0.75, 1)(b) (ˆ’1.08, ˆ’0.30, 0.01, 0.35, 1.27)(c) (0.64, 27.25, 53.16, 100, 275.7)(d)
Match each standard deviation with one of the histograms inFigure 2.23.(a) s = 0.5(b) s = 10(c) s = 50(d) s = 1(e) s = 1000(f) s = 0.29The standard deviations with the histograms. -3 -1 2 3 0.0 0.4
Match the three standard deviations s = 1, s = 3, and s = 5 with the three histograms inFigure 2.22.The standard deviations with the histograms -5 0 5 10 15 20 25 (a) Histogram A 20 25 (b) Histogram
The variable TV, number of hours spent watching television per week, in the StudentSurvey dataset.Use technology to find the following values:(a) The mean and the standard deviation.(b) The five
The variable Exercise, number of hours spent exercising per week, in the StudentSurvey dataset.Use technology to find the following values:(a) The mean and the standard deviation(b) The five number
Table 2.18 shows the number of women (per 1000) between 15 and 44 years of age who have been married grouped by the number of children they have had. Table 2.19 gives the same information for women
Calculate the mean and the median for the numbersWhich do you think is a better measure of center for this set of values? Why? (There is no right answer, but think about which you would use.) 1, 1,
Describe one quantitative variable that you believe will give data that are skewed to the right, and explain your reasoning. Do not use a variable that has already been discussed.
Give any set of five numbers satisfying the condition that:(a) The mean of the numbers is substantially less than the median.(b) The mean of the numbers is substantially more than the median.(c) The
Apparently, sexual frustration increases the desire for alcohol, at least in fruit flies. Scientists randomly put 24 fruit flies into one of two situations. The 12 fruit flies in the ‘‘mating”
In Exercise 2.24 on page 57, we saw that those with a college degree were much more likely to be employed. The same article also gives statistics on earnings in the US in 2009 by education level. The
Often we are interested not just in a single mean but in a difference in means between two groups. In the Student Survey data, there are 36 seniors: 26 males and 10 females. Table 2.17 gives the
A survey conducted in May 2010 asked 1917 cell phone users to estimate, on average, the number of text messages sent and received per day.(a) Do you expect the distribution of number of text messages
The plasma beta-carotene level (concentration of beta-carotene in the blood), in ng/ml, was measured for a sample of n = 315 individuals, and the results are shown in the histogram inFigure 2.15.(a)
The number of grams of fiber eaten in one day for a sample of ten people are(a) Find the mean and the median for these data.(b) The value of 115 appears to be an obvious outlier. Compute the mean and
Life expectancy for all the different countries in the world ranges from a low of only 43.9 years (in Afghanistan) to a high of 82.8 years (in San Marino). Life expectancies are clustered at the high
€˜€˜Are natural languages neutrally, positively, or negatively biased?€ That is the question a recent study set out to answer. They found the top 5000 words used in
Consider a dataset giving the adult weight of species of insects. Most species of insects weigh less than 5 grams, but there are a few species that weigh a great deal, including the largest insect
It is commonly believed that normal human body temperature is 98.6—¦F (or 37—¦C). In fact, €˜€˜normal€ temperature can vary from person to
Arsenic is toxic to humans, and people can be exposed to it through contaminated drinking water, food, dust, and soil. Scientists have devised an interesting new way to measure a person€™s
The average number of television sets owned per household for all households in the US is 2.6.The correct notation for the mean.
The average number of yards per punt for all punts in the National Football League is 41.5 yards.The correct notation for the mean.
The average number of text messages sent or received in a day was 60, in a survey of n = 799 teen cell phone users conducted in June 2011The correct notation for the mean.
The average number of calories eaten in one day is 2386 calories for a sample of 100 participants.The correct notation for the mean.
Clearly skewed to the right.Draw any dotplot to show a dataset.
Approximately symmetric but not bell-shaped.Draw any dotplot to show a dataset.
Approximately symmetric and bell-shaped.Draw any dotplot to show a dataset.
Clearly skewed to the left.Draw any dotplot to show a dataset.
Does alcohol increase reaction time? Design a randomized experiment to address this question using the method described in each case. Assume the participants are 40 college seniors and the response
The US Department of Transportation announces that of the 250 million registered passenger vehicles in the US, 2.1% are electro-gas hybrids.State whether the data are best described as a population
A subscription-based music website tracks its total number of active users.State whether the data are best described as a population or a sample.
Send an email to a random sample of students at a university asking them to reply to the question: ‘‘Do you think this university should fund an ultimate frisbee team?” A small number of
In Data 1.4 on page 24, we describe the results of a question asked by a national newspaper columnist: ‘‘If you had it to do over again, would you have children?” In addition to those results
‘‘Do metal tags on penguins harm them?”We describe data collection methods. Indicate whether the data come from an experiment or an observational study.
About 60% of a child’s growth hormone is secreted during sleep, so it is believed that a lack of sleep in children might stunt growth.(a) What is the explanatory variable and what is the response
It is commonly accepted that athletes should ‘‘carbo load,” that is, eat lots of carbohydrates, the day before an event requiring physical endurance. Is there any truth to this? Suppose you
Causation does not necessarily mean that there is no confounding variable. Give an example of an association between two variables that have a causal relationship AND have a confounding variable.
The survey students consisted of 169 females and 193 males. Find p̂ , the proportion who are female.Find the sample proportion p̂.
The survey included 43 students who smoke and 319 who don’t. Find p̂, the proportion who smoke.Find the sample proportion p̂.
Of the students who identified their class year in the survey, 94 were first years, 195 were sophomores, 35 were juniors, and 36 were seniors. Find p̂, the proportion who are upperclass students
The math SAT score is higher than the verbal SAT score for 205 of the 355 students who answered the questions about SAT scores. Find p̂, the proportion for whom the math SAT score is higher.Find the
In the 2010 US Census, we see that 37,342,870 people, or 12.4% of all residents, are foreign-born.Give the relevant proportion using correct notation.
A recent headline states that ‘‘73% say Woman President Likely in Next 10 Years.” The report gives the results of a survey of 1000 randomly selected likely voters in the US.Give the relevant
A survey conducted of 1502 randomly selected US adults found that 931 of them believed the government does not provide enough support for soldiers returning from Iraq or Afghanistan.Give the relevant
Of all 1,547,990 members of the high school class of 2010 who took the SAT(Scholastic Aptitude Test), 1,114,273 were from a public high school.Give the relevant proportion using correct notation.
Of the 362 students who answered the question about what award they would prefer, 31 preferred an Academy Award, 149 preferred a Nobel Prize, and 182 preferred an Olympic gold medal.Construct a
Of the 361 students who answered the question about the number of piercings they had in their body, 188 had no piercings, 82 had one or two piercings, and the rest had more than two.Construct a
Twenty cases:Cases are classified according to one variable, with categories A and B, and also classified according to a second variable with categories 1, 2, and 3. The cases are shown, with the
Thirty cases:Cases are classified according to one variable, with categories A and B, and also classified according to a second variable with categories 1, 2, and 3. The cases are shown, with the
Rock-Paper-Scissors, also called Roshambo, is a popular two-player game often used to quickly determine a winner and loser. In the game, each player puts out a fist (rock), a flat hand (paper), or a

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