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mathematics
statistics the art and science

Questions and Answers of Statistics The Art and Science

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.
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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,
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
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
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
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
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
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 Ïƒ2=
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
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
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
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
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
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,
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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:
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
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
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
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
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
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
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
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
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
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
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
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
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

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