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mathematics
statistics the art and science
Statistics The Art And Science Of Learning From Data 4th Edition Alan Agresti, Christine A. Franklin, Bernhard Klingenberg - Solutions
A Harris Poll of 2300 U.S. adults surveyed online in April 2014 reports that 43% regularly watch television shows through streaming.a. Find a 95% confidence interval and interpret it in context.b. Would a 99% confidence interval result in a wider or narrower interval? Explain.c. If the survey had
The Department of Public Health at the University of Western Australia conducted a survey in which they randomly sampled general practitioners (GP) in Australia. One question asked whether the GP had ever studied alternative therapy, such as acupuncture, hypnosis, homeopathy, and yoga. Of 282
Refer to the previous exercise. The following printout shows results for the females in the sample, where X = the number answering yes. Explain how to interpret each item, in context.Previous exerciesThe variable POSTLIFE in the 2012 General Social Survey asked, €œDo you believe in life
The variable POSTLIFE in the 2012 General Social Survey asked, “Do you believe in life after death?” A report based on these data stated that “81% of Americans believe in life after death. The margin of error for this result is plus or minus 1.8%.” Explain how you could form a 95%
After the British monarchy celebrated its diamond jubilee in 2012, a July poll conducted by YouGov.com and the Sunday Times of 1,667 British residents showed that 86% think the Queen personally has done a good job during her time on the throne, and 73% think that Britain should continue to have a
In July 2014, midway through his second term as president, Gallup estimated Obama’s approval rate at 42%. According to gallup.com, “. . . Results are based on telephone interviews with approximately 1,500 national adults; margin of error is ±3 percentage points.” How could you explain the
The U.S Bureau of the Census reports that based on data from the American Community Survey in 2012, 3.6 percent of all college graduates between the ages of 25 and 64 were unemployed. A larger percentage of men than women were unemployed: 3.7 percent and 3.5 percent, respectively.a. Are these point
In 2014, the General Social Survey interviewed 1399 randomly selected U.S. residents about how much time per week they spent surfing the web. The responses revealed a very right-skewed distribution, with a sample mean of 12 hours and a standard deviation of 15 hours, indicating that the population
Explain the purpose of using the bootstrap method.
Google started selling Google Glass (a type of wearable technology that projects information onto the eye) in the United States in spring 2014 for $1500. A national poll reveals that out of 500 people sampled, nobody owned Google Glass.a. Find the sample proportion who don’t own Google Glass and
The Palestinian Central Bureau of Statistics (www.pcbs.gov.ps) asked mothers of age 20–24 about the ideal number of children. For those living on the Gaza Strip, the probability distribution is approximately P(1) = 0.01, P(2) = 0.10, P(3) = 0.09, P(4) = 0.31, P(5) = 0.19, and P(6 or more) = 0.29.
Access the Sampling Distribution of the Sample Proportion web app. When p = 0.6 and the sample size n = 3, the mean and standard deviation of the sampling distribution (given in the table in part a of Exercise 7.51) are equal to 0.6 and 0.283. With the app, simulate the sampling distribution by
The sampling distribution of a sample mean for a random sample size of 100 describesa. How sample means tend to vary from random sample to random sample of size 100.b. How observations tend to vary from person to person in a random sample of size 100.c. How the data distribution looks like the
In a class of 150 students, the professor has each person toss a fair coin 50 times and calculate the proportion of times the tosses come up heads. Roughly 95% of students should have proportions between which two numbers?a. 0.49 and 0.51b. 0.05 and 0.95c. 0.42 and 0.58d. 0.36 and 0.64e. 0.25 and
The central limit theorem impliesa. All variables have approximately bell-shaped data distributions if a random sample contains at least about 30 observations.b. Population distributions are normal whenever the population size is large.c. For sufficiently large random samples, the sampling
Which of the following is not correct? The standard deviation of a statistic describesa. The standard deviation of the sampling distribution of that statistic.b. The standard deviation of the sample data measurements.c. How close that statistic falls to the parameter that it estimates.d. The
Access the Sampling Distribution of the Sample Proportion web app.a. For p = 0.5 and a sample of size n = 3, the graph of the sampling distribution is given below. (This is the graph corresponding to the table in Exercise 7.49, part b.) Compute the mean of the sampling distribution from first
Refer to the previous two exercises but now suppose the population proportion in Boston preferring pizza A is p = 0.6 instead of p = 0.5. (Then, the eight possible outcomes (AAA, AAD, . . . , DDA, DDD) of a sample of size n = 3 are not equally likely, as in part b of Exercise 7.49)a. Use the
Refer to the previous exercise, in which the proportion of people preferring pizza A is p = 0.5 and a sample of size n = 3 is taken. The sampling distribution of the sample proportion of people preferring pizza A as shown in part b of that exercise can also be derived using the binomial
Explain how the standard deviation of the sampling distribution of a sample proportion gives you useful information to help gauge how close a sample proportion falls to the unknown population proportion.
An executive in an Australian savings bank decides to estimate the mean amount of money withdrawn in bank machine transactions. From past experience, she believes that $50 (Australian) is a reasonable guess for the standard deviation of the distribution of withdrawals. She would like her sample
Refer to the previous exercise, in which the manufacturer will return the entire shipment if more than 5% defective chips are found in the sample.a. Find the probability that the shipment will be returned if the manufacturer decides to test only 380 randomly selected chips (instead of 500).b.
A supplier of electronic chips for tablets claims that only 4% of his chips are defective. A manufacturer tests 500 randomly selected chips from a large shipment from the supplier for potential defects.a. Find the mean and standard deviation for the distribution of the sample proportion of
According to the Alzheimer’s Association, 2 as of 2014 Alzheimer’s disease affects 1 in 9 Americans over the age of 65. A study is planned of health problems the elderly face. For a random sample of Americans over the age of 65, report the shape, mean, and standard deviation of the sampling
Access the Sampling Distribution of the Sample Mean web app and select Bell-Shaped for the shape of the population distribution, which looks similar to the fourth column in Figure 7.11. Select a value for the population mean and standard deviation. Is the sampling distribution normal even for n =
When you flip a balanced coin twice, three things can happen: 0 heads, 1 head, or 2 heads. Since there are three possible outcomes, they each have probability 1/3. (This was claimed by the French mathematician, Jean le Rond d’ Alembert, in 1754. To reason this, write down the sample space for the
Your class can use the capture–recapture method described in the previous exercise to estimate the number of goldfish in a bag of Cheddar Goldfish. Pour the Cheddar Goldfish into a paper bag, which represents the pond. Sample 10 of them. For this initial sample, use Pretzel Goldfish to replace
An analysis of published medical studies about heart attacks (Crossen, 1994, p. 168) noted that in the studies having randomization and strong controls for bias, the new therapy provided improved treatment 9% of the time. In studies without randomization or other controls for bias, the new therapy
Let€™s use the Sampling Distribution of the Sample Mean web app accessible from the book€™s website to show that the first population distribution shown in Figure 7.11 has a more nearly normal sampling distribution for the mean as n increases. Select uniform for the population
The previous exercise mentions that the duration of your phone calls follows a distribution with mean μ = 2.8 minutes and standard deviation σ = 2.1 minutes. From a random sample of n = 45 calls, your parents computed a sample mean of x̅ = 3.4 minutes and a sample standard deviation of s = 2.9
A recent personalized information sheet from your wireless phone carrier claims that the mean duration of all your phone calls was μ = 2.8 minutes with a standard deviation of σ = 2.1 minutes.a. Is the population distribution of the duration of your phone calls likely to be bell shaped, right-,
Access the Sampling Distribution of the Sample Mean (discrete variable) web app on the book’s website. Enter the probabilities P1X = x2 of 0.1667 for the numbers 1 through 6 to specify the probability distribution of a fair die. (This is a discrete version of the uniform distribution shown in the
Assume that the distribution of the score on a recent midterm is bell shaped with population mean m = 70 and population standard deviation s = 10. You randomly sample n = 12 students who took the midterm. Using the Sampling Distribution of the Sample Mean web app accessible on the book’s
A student running for a position in student government believes that 55% of the student body will vote for her. However, she is worried about low voter turnout.a. Assuming she truly has 55% support in the entire student body, find the mean and standard deviation of the sampling distribution for the
a. With random sampling, does the shape of the data distribution tend to resemble more closely the sampling distribution or the population distribution? Explain.b. Is the sampling distribution of the sample proportion always bell shaped? Investigate with the Sampling Distribution app by setting n =
At a university, 60% of the 7,400 students are female. The student newspaper reports results of a survey of a random sample of 50 students about various topics involving alcohol abuse, such as participation in binge drinking. They report that their sample contained 26 females.a. Explain how you can
Consider the sampling distribution you were simulating in parts a and b of the previous exercise, assuming p = 0.10 with samples of size 500 each. Using the appropriate formulas from this section, find the mean and the standard deviation of the sampling distribution of the sample proportion:a. For
A company that is selling condos in Florida plans to send out an advertisement for the condos to 500 potential customers, in which they promise a free weekend at a resort on the Florida coast in exchange for agreeing to attend a four-hour sales presentation. The company would like to know how many
For the 68 World Series played between 1945 and 2013, 13 (19%) ended after 4 games, 12 (18%) after 5 games, 15 (22%) after 6 games, and 28 (41%) needed to go all the way to 7 games.a. Find the average number of games played based on these data. (Remember from Section 6.1 that the mean for the
Exercise 6.47 discussed the record losing streak of the Pittsburgh Pirates. In particular, if the Pirates’ chance of winning any single game is 0.42, then atthe beginning of a new season, the probability of them winning at least 81 games, and hence not adding another losing season to the streak,
Assume prices for used Audi A4s available on carmax.com follow a normal distribution with mean $23,800 and standard deviation $4,380.a. Prices quoted on carmax.com are without sales tax. To account for a 6% sales tax, you multiply each price by 1.06. What is the distribution of these new prices
The previous exercise gave the formula for the standard deviation of a discrete random variable X. Let’s look at a simple case. Suppose X is a binary random variable where X = 1 with probability p and X = 0 with probability (1 - p).a. Show that the mean of X is equal to p. b. Since (x - ц)2
The variance of a probability distribution of a random variable is a weighted average of its squared distances from the mean m. For discrete random variables, it equals σ2= Σ(x - μ)2P(x). Multiply each possible squared deviation (x - μ)2by its
The National Center for Educational Statistics reported that in 2012 the ACT college placement and admission examination had a mean of 21.1 and standard deviation of 5.3. a. Which probability distribution would you expect to be more appropriate for describing the scores: the normal or the
On 9/11/2002, the first anniversary of the terrorist destruction of the World Trade Center in New York City, the winning three-digit New York State Lottery number came up 9-1-1. The probability of this happening wasa. 1/1000.b. (1/1000)2 = 0.000001.c. 1 in a billion.d. 3/10.
A question has four possible answers, only one of which is correct. You randomly guess the correct response. With 20 such questions, the distribution of the number of incorrect answersa. Is binomial with n = 20 and p = 0.25.b. Is binomial with n = 20 and p = 0.50.c. Has mean equal to 10.d. Has
Let X denote the response of a randomly selected person to the question, €œWhat is the ideal number of children for a family to have?€ The probability distribution of X in the United States is approximately as shown in the table, according to the gender of the person asked the
For the normal distributions shown below, use Table A, software, or a calculator to find the probability that an observation falls in the shaded region.a.b. H + 0.670 μ-0.5σ μ μ+0.5σ
Suppose that weekly use of gasoline for motor vehicle travel by adults in North America has approximately a normal distribution with a mean of 20 gallons and a standard deviation of 6 gallons. Many people who worry about global warming believe that Americans should pay more attention to energy
Example 2 gave the probability distribution for the number of games played in a best out of seven series between teams A and B. Let’s derive the probability distribution for a best of five series, in which the team that gets 3 wins first wins the entire series.a. Write out the sample space of all
The retail chain from the previous exercise decides to follow up its first ad with a second one, again to 15 million Facebook users. This time it gives away a $1 online credit for every user who likes the ad. Now, assume the probability is 0.0005 that a user will like it.a. Find the mean and
A large retail chain sends out an ad about a new product to 15 million users on Facebook and asks them to like the message. Assume the probability that a user will like the message (instead of ignoring it) is 0.00001.a. State assumptions for a binomial distribution to apply for X = the number of
According to a study done by the Lucy Stone League and reported by ABC News 9 in February 2011, 90% of brides take the surname of their new husband. Ann notes that of her four best friends who recently married, none kept her own name. If they had been a random sample of brides, how likely would
In the United States in 2002, about 43,000 people died in auto crashes and 0 people died in commercial airline accidents. G. Gigerenzer (2002, p. 31) states, “The terrorist attack on September 11, 2001, cost the lives of some 3,000 people. The subsequent decision of millions to drive rather than
Since events of low probability eventually happen if you observe enough trials, a monkey randomly pecking on a typewriter could eventually write a Shakespeare play just by chance. Let’s see how hard it would be to type the title of Macbeth properly. Assume 50 keys for letters and numbers and
A simple way for a company to raise money to fund its operations is by selling corporate bonds. Suppose an investor buys a bond from a company for $7500. As part of the terms of the bond, the company will repay the investor $2000 at the end of each of the next five years. It seems like a good deal
You consider your birth date to be special since it falls on January 1. Suppose your class has 25 students.a. Is the probability of finding at least one student with a birthday that matches yours greater, the same, or less than the probability found in Example 13 of a match for at least two
Airplane safety has been improving over the years. From 2000 to 2010, the average number of global airline deaths per year was over 1000, even when excluding the nearly 3000 deaths in the United States on September 11, 2001. The number of global airline deaths declined in 2011, again in 2012, and
You randomly sample 10 people in your school, and none of them is a vegetarian. Does this mean that the probability of being a vegetarian for students at your school equals 0? Explain.
Explain what is meant by the long-run relative frequency definition of probability.
A study (N. Schwarz et al., Public Opinion Quarterly, vol. 49, 1985, p. 388) asked German adults how many hours a day they spend watching TV on a typical day. When the possible responses were the six categories (up to 0.5 hour, 0.5 to 1 hour, 1 to 1.5 hours, . . . , more than 2.5 hours), 16% of
In 1995 in the United Kingdom, the Equality Code used by the legal profession added a section to make members more aware of sexual harassment. It states that “research for the Bar found that over 40 percent of female junior tenants said they had encountered sexual harassment during their time at
An Internet poll conducted in the United Kingdom by Netdoctor.co.uk asked individuals to respond to an “emotional health survey” (see www.hfienberg.com/clips/pollspiked.htm). There were 400 volunteer respondents. Based on the results, the British Broadcasting Corporation (BBC) reported that
When the Yankelovich polling organization asked, “Should laws be passed to eliminate all possibilities of special interests giving huge sums of money to candidates?” 80% of the sample answered yes. When they posed the question, “Should laws be passed to prohibit interest groups from
A recent General Social Survey asked subjects whether they supported legalized abortion in each of seven circumstances. The percentage who supported legalization varied between 44.6% (if the woman is not married) to 88.6% (if the woman’s health is seriously endangered by the pregnancy). This
A simple random sample of size n is one in whicha. Every nth member is selected from the population.b. Each possible sample of size n has the same chance of being selected.c. There is exactly the same proportion of women in the sample as is in the population.d. You keep sampling until you have a
Many research studies focus on a link between marijuana use and psychotic disorders such as schizophrenia. Studies have found that people with schizophrenia are twice as likely to smoke marijuana as those without the disorder. Data also suggest that individuals who smoke marijuana are twice as
In 2014, the Pittsburgh Penguins were ahead of the New York Rangers three games to one in the first round of the National Hockey League playoffs. ESPN.com conducted a voluntary, online poll that asked respondents to predict the outcomes of the rest of the series. Of all 1,094 respondents, 52% said
Carol Dweck is a noted psychologist from Stanford who believes that we should praise students’ effort and not their intelligence. In her seminal study (2006), she gave students a test and then randomly divided the students into two groups. She praised the effort of one group and praised the
Example 1 in Chapter 3 described a survey of 1314 women during 1972–1974, in which each woman was asked whether she was a smoker. Twenty years later, a follow-up survey observed whether each woman was deceased or still alive. Was this study a retrospective study or a prospective study? Explain.
The contingency table shows results from the German study about whether there was an association between mobile phone use and eye cancer (Stang et al., 2001).a. The study was retrospective. Explain what this means.b. Explain what is meant by cases and controls in the headings of the table.c. What
Of 400 employees at a company, 25% work in production, 40% work in sales and marketing, and 35% work in new product development. As part of a security awareness training program, the group overseeing implementation of the program will randomly choose a sample of 20 employees to begin the training;
Revisit the setting of Exercise 4.37. Suppose that in addition to the participants being blinded, the researchers responsible for recording the results of the study are also blinded. Why does it matter whether the researchers know which participants receive which treatment?
A recent study (J Child Fam Stud, DOI 10.1007/s10826-014-9949-9) found that children in Singapore who had a closer relationship with their parents played fewer hours of video games per week and had fewer pathological symptoms of video-gaming.a. What is the population of interest for this survey?b.
The 2013–2014 Recruiting Trends report, produced each year by Michigan State University, reports that hiring over the past year of people with a bachelor’s degree increased 7%, for people with a PhD increased 26%, and for people with an MBA decreased 25%. This was based on a voluntary poll of
The website www.ratemyprofessors .com provides students an opportunity to view ratings for instructors at their universities. A group of students planning to register for a statistics course in the upcoming semester are trying to identify the instructors who receive the highest ratings on the site.
Use an app or computer program to select 10 of the 60 school district accounts described in Example 5. Explain how you did this and identify the accounts to be sampled
In Example 4, a random drawing was held to select the winners of the football tickets. Organizers randomly chose numbers, using the computer to generate the sample randomly. Choose another sample by using either the Random Numbers web app from the book’s website, the website random.org, or
Refer to the previous exercise. Suppose carmax.com decides to highlight any used car that is priced 1.5 standard deviations below the mean price as a special deal on its Web site.a. If the distribution of used-car prices is normal, what percentage of used Audi A4s will be highlighted?b. If the
Data from the Web site carmax.com compiled in July 2014 show that prices for used Audi A4 cars advertised on the Web site have a mean of $23,800 and a standard deviation of $4,380. Assume a normal distribution for the price.a. What percent of used Audi A4s cost more than $25,000?b. What percent of
For 5459 pregnant women using Aarhus University Hospital in Denmark in a two-year period who reported information on length of gestation until birth, the mean was 281.9 days, with standard deviation 11.4 days. A baby is classified as premature if the gestation time is 258 days or fewer. (Data from
In the National Basketball Association, the top free throw shooters usually have probability of about 0.90 of making any given free throw.a. During a game, one such player (Dirk Nowitzki) shot 10 free throws. Let X = number of free throws made. What must you assume for X to have a binomial
For each of the following situations, explain whether the binomial distribution applies for X.a. You are bidding on four items available on eBay. You think that you will win the first bid with probability 25% and the second through fourth bids with probability 30%. Let X denote the number of
You are bidding on four items available on eBay. You think that for each bid, you have a 25% chance of winning it, and the outcomes of the four bids are independent events. Let X denote the number of winning bids out of the four items you bid on.a. Explain why the distribution of X can be modeled
Refer to the previous exercise. Let the random variable X = number of compatible donors. Check the conditions for X to be binomial by answering parts a–c.a. What constitutes a trial, how many trials are there, and how many outcomes does each trial have?b. Does each trial have the same probability
In kidney transplantations, compatibility between donor and receiver depends on such factors as blood type and antigens. Suppose that for a randomly selected donor from a large national kidney registry, there is a 10% chance that he or she is compatible with a specific receiver. Three donors are
Over roughly the past 100 years, the mean monthly April precipitation in Williams town, Massachusetts, equaled 3.6 inches with a standarddeviation of 1.6 inches. (Source: http://web.williams.edu/ weather/)a. In April 1983, the wettest April on record, the precipitation equaled 8.4 inches.
In the United States, the mean birth weight for boys is 3.41 kg, with a standard deviation of 0.55 kg. (Source: cdc.com.) Assuming that the distribution of birth weight is approximately normal, find the following using a table, calculator, or software.a. A baby is considered of low birth weight if
Suppose your favorite coffee machine offers 12 ounce cups of coffee. The actual amount of coffee put in the cup by the machine varies according to a normal distribution, with mean equal to 13 ounces and standard deviation equal to 0.6 ounces. For each question below, sketch a graph, mark the mean,
A World Health Organization study (the MONICA project) of health in various countries reported that in Canada, systolic blood pressure readings have a mean of 121 and a standard deviation of 16. A reading above 140 is considered high blood pressure.a. What is the z-score for a blood pressure
A random number generator is used to generate a real number between 0 and 1, equally likely to fall anywhere in this interval of values. (For instance, 0.3794259832c is a possible outcome.)a. Sketch a curve of the probability distribution of this random variable, which is the continuous version of
Some companies, such as Demand Tec, have developed software to help retail chains set prices that optimize their profits. An Associated Press story (April 28, 2007) about this software described a case in which a retail chain sold three similar power drills: one for $90, a better one for $120, and
You are watching two items posted for sale on eBay and bid $30 for the first and $20 for the second item. You estimate that you are going to win the first bid with probability 0.1 and the second bid with probability 0.2, and you assume that winning the two bids are independent events. Let X denote
The previous exercise on roulette described two bets: one bet on the single number 23 with winnings of either $350 or - $10 and a different bet on black with winnings of either $10 or - $10. For both types of bets, the expected winning is - $0.53. Which of the two bets has the larger standard
In a best out of three series played between teams A and B, the team that gets two wins first wins the entire series. Assuming that team A has a 70% chance of winning a game and that outcome of games are independent events, the probability that the series ends after two games is 58%.a. Find the
You plan to purchase dental insurance for your three remaining years in school. The insurance makes a one-time payment of $1,000 in case of a major dental repair (such as an implant) or $100 in case of a minor repair (such as a cavity). If you don’t need dental repair over the next 3 years, the
Refer to the previous exercise. Over the course of a season, this player shoots 400 free throws.a. Find the mean and standard deviation of the probability distribution of the number of free throws he makes.b. By the normal distribution approximation, within what range would you expect the number
Mammography is estimated to save about 1 life in every 1000 women. “Participating in annual mammography screening … has roughly the same effect on life expectancy as reducing the distance one drives each year by 300 miles” (Gigerenzer 2002, pp. 60, 73). Which of the following do you think has
You have a dream in which you see your favorite movie star in person. The very next day, you are visiting Manhattan and you see her walking down Fifth Avenue.a. This is such an incredibly unlikely coincidence that you should report it to your local newspaper.b. This is somewhat unusual, but given
A balanced coin is flipped 100 times. By the law of large numbers:a. There will almost certainly be exactly 50 heads and 50 tails.b. If we got 100 heads in a row, almost certainly the next flip will be a tail.c. For the 100 flips, the probability of getting 100 heads equals the probability of
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