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Introductory Statistics Exploring The World Through Data 2nd Edition Robert Gould, Colleen Ryan - Solutions

A married couple plans to have four children, and they are wondering how many boys they should expect to have. Assume none of the children will be twins or other multiple births. Also assume the probability that a child will be a boy is 0.50. Explain why this is a binomial experiment. Check all
A coin will be flipped three times, and the number of heads recorded. Explain why this is a binomial experiment. Check all four required conditions.
Toss a fair six-sided die. The probability density function (pdf) in table form is given. Make a graph of the pdf for the die.
For each situation, identify the sample size n, the probability of success p, and the number of successes x. When asked for the probability, state the answer in the form b(n, p, x). There is no need to give the numerical value of the probability. Assume the conditions for a binomial experiment are
For each situation, identify the sample size n, the probability of success p, and the number of successes x. When asked for the probability, state the answer in the form b(n, p, x). There is no need to give the numerical value of the probability. Assume the conditions for a binomial experiment
According to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered. (In contrast, only 2% of bikes stolen in New York City are recovered.) Find the probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered.
The three-year recidivism rate of parolees in Florida is about 30%; that is, 30% of parolees end up back in prison within three years (www.floridaperforms.com). Assume that whether one parolee returns to prison is independent of whether any of the others returns.a. Find the probability that exactly
The undergraduate admission rate at Harvard University in 2012 was 6%.a. Assuming the admission rate is still 6%, in a sample of 100 applicants to Harvard, what is the probability that exactly 5 will be admitted? Assume that decisions to admit are independent.b. What is the probability that exactly
The undergraduate admission rate at Cornell University in 2012 was 16%.a. Assuming the admission rate is still 16%, in a sample of 100 applicants to Cornell, what is the probability that exactly 15 will be admitted?b. What is the probability that exactly 85 out of 100 independent applicants will be
Wisconsin has the highest high school graduation rate of all states at 90%.a. In a random sample of 10 Wisconsin high school students, what is the probability that 9 will graduate?b. In a random sample of 10 Wisconsin high school students, what is the probability than 8 or fewer will graduate?c.
When a certain type of thumbtack is flipped, the probability of its landing tip up (U) is 0.60 and the probability of its landing tip down (D) is 0.40. Now suppose we flip two such thumbtacks: one red, one blue. Make a list of all the possible arrangements using U for up and D for down, listing the
Colorado has a high school graduation rate of 75%.a. In a random sample of 15 Colorado high school students, what is the probability that exactly 9 will graduate?b. In a random sample of 15 Colorado high school students, what is the probability that 8 or fewer will graduate?c. What is the
The homicide clearance rate in Florida is 60%. A crime is cleared when an arrest is made, a crime is charged, and the case is referred to a court.a. What is the probability that exactly 6 out of 10 independent homicides are cleared?b. Without doing a calculation, state whether the probability that
The homicide clearance rate in Virginia is 74%. A crime is cleared when an arrest is made, a crime is charged, and the case is referred to a court.a. What is the probability that 7 or fewer out of 10 independent homicides are cleared?b. What is the probability that 7 or more out of 10 independent
In New Mexico, about 70% of drivers who are arrested for driving while intoxicated (DWI) are convicted (www.drunkdrivingduilawblog.com).a. If 15 independently selected drivers were arrested for DWI, how many of them would you expect to be convicted?b. What is the probability that exactly 11 out of
A 2013 Gallup poll indicated that about 80% of U.S. households had access to a high-speed Internet connection.a. Suppose 100 households were randomly selected from the United States. How many of the households would you expect to have access to a high-speed Internet connection?b. If 10 households
You may have heard that drunk driving is dangerous, but what about drunk walking? According to federal information (reported in the Ventura County Star on August 6, 2013), 50% of the pedestrians killed in the United States had a blood-alcohol level of 0.08% or higher. Assume that two randomly
According to a Pew poll in 2012, 58% of high school seniors admit to texting while driving. Assume that we randomly sample two seniors of driving age. a. If a senior has texted while driving, record Y; if not, record N. List all possible sequences of Y and N. b. For each sequence, find by hand the
A fair coin is flipped 50 times. a. What is the expected number of heads? b. Find the standard deviation for the number of heads. c. How many heads should you expect, give or take how many? Give the range of the number of heads based on these numbers.
According to GMAC Insurance, 20% of drivers aged 60–65 fail the written drivers’ test. This is the lowest failure rate of any age group. If 200 people aged 60–65 independently take the exam, how many would you expect to pass? Give or take how many?
In Toronto, Canada, 55% of people pass the drivers’ road test. Suppose that every day, 100 people independently take the test. a. What is the number of people who are expected to pass? b. What is the standard deviation for the number expected to pass? c. After a great many days, according to the
When a fair coin is flipped, the probability of its landing heads (H) is 0.50 and the probability of its landing tails (T) is also 0.50. Make a list of all the possible arrangements for flipping a fair coin twice, using H for heads and T for tails. Find the probabilities of each arrangement, and
Toronto drivers have been going to small towns in Ontario (Canada) to take the drivers’ road test, rather than taking the test in Toronto, because the pass rate in the small towns is 90%, which is much higher than the pass rate in Toronto. Suppose that every day, 100 people independently take the
A study of U.S. births published on the website Medscape from WebMD reported that the average birth length of babies was 20.5 inches and the standard deviation was about 0.90 inch. Assume the distribution is approximately Normal. Find the percentage of babies with birth lengths of 22 inches or less.
A study of U.S. births published on the website Medscape from WebMD reported that the average birth length of babies was 20.5 inches and the standard deviation was about 0.90 inch. Assume the distribution is approximately Normal. Find the percentage of babies who have lengths of 19 inches or less
A study of human body temperatures using healthy men showed a mean of 98.1°F and a standard deviation of 0.70°F. Assume the temperatures are approximately normally distributed.a. Find the percentage of healthy men with temperatures below 98.6°F (that temperature was considered typical for many
A study of human body temperatures using healthy women showed a mean of 98.4°F and a standard deviation of about 0.70°F. Assume the temperatures are approximately normally distributed.a. Find the percentage of healthy women with temperatures below 98.6°F (this temperature was considered typical
Cremation rates have been increasing. In Nevada the cremation rate is 70%. Suppose that we take a random sample of 400 deaths in Nevada.a. How many of these decedents would you expect to be cremated?b. What is the standard deviation for the number to be cremated?c. How many would you expect not to
Cremation rates have been increasing in the United States. Mississippi is the state with the lowest rate, which is 10%. Suppose that we take a random sample of 900 deaths in Mississippi and that the decision to be cremated is made independently. a. How many of the 900 decedents would you expect to
Babies weighing 5.5 pounds or less at birth are said to have low birth weights, which can be dangerous. Full-term birth weights for single babies (not twins or triplets or other multiple births) are normally distributed with a mean of 7.5 pounds and a standard deviation of 1.1 pounds.a. For one
The distribution of the math portion of SAT scores has a mean of 500 and a standard deviation of 100, and the scores are approximately normally distributed.a. What is the probability that one randomly selected person will have an SAT score of 550 or more?b. What is the probability that four
Babies in the United States have a mean birth length of 20.5 inches with a standard deviation of 0.90 inch. The shape of the distribution of birth lengths is approximately Normal.a. How long is a baby born at the 20th percentile?b. How long is a baby born at the 50th percentile?c. How does your
a. From your answers in Exercise 6.7, find the probability of getting 0 ups, 1 up, or 2 ups when flipping two thumbtacks, and report the distribution in a table.b. Make a probability distribution graph of this.
Babies in the United States have a mean birth length of 20.5 inches with a standard deviation of 0.90 inch. The shape of the distribution of birth lengths is approximately Normal.a. Find the birth length at the 2.5th percentile.b. Find the birth length at the 97.5th percentile.c. Find the z-score
You need to select a simple random sample of four from eight friends who will participate in a survey. Assume the friends are numbered 1, 2, 3, 4, 5, 6, 7, and 8.Select four friends, using the two lines of numbers in the next column from a random number table. Read off each digit, skipping any
Assume your class has 30 students and you want a random sample of 10 of them. Describe how to randomly select 10 people from your class using the random number table.
In carrying out a study of views on capital punishment, a student asked a question two ways:1. With persuasion: €œMy brother has been accused of murder and he is innocent. If he is found guilty, he might suffer capital punishment. Now do you support or oppose capital
Use the data given in Exercise 7.17.Make the two given tables into one table by combining men for capital punishment into one group, men opposing it into another, women for it into one group, and women opposing it into another. Show your two-way table.The student who collected the data could have
a. If a rifleman’s gunsight is adjusted incorrectly, he might shoot bullets consistently close to 2 feet left of the bull’s-eye target. Draw a sketch of the target with the bullet holes. Does this show lack of precision or bias?
a. If a rifleman’s gunsight is adjusted correctly but he has shaky arms, the bullets might be scattered widely around the bull’s-eye target. Draw a sketch of the target with the bullet holes. Does this show variation (lack of precision) or bias? b. Draw a second sketch of the target if the
Suppose that, when taking a random sample of three students’ GPAs, you get a sample mean of 3.90. This sample mean is far higher than the college-wide (population) mean. Does that prove that your sample is biased? Explain. What else could have caused this high mean?
Suppose you attend a school that offers both traditional courses and online courses. You want to know the average age of all the students. You walk around campus asking those students that you meet how old they are. Would this result in an unbiased sample?
A large collection of one-digit random numbers should have about 50% odd and 50% even digits, because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8).a. Find the proportion of odd-numbered digits in the following lines from a random number table. Count
Consider a 30-digit line from a random number table.1, 3, 5, 7, and 9 are odd and 0, 2, 4, 6, and 8 are even. a. How many of the 30 digits would you expect to be odd, on average?b. If you actually counted, would you get exactly the number you predicted in part a? Explain.
According to the Mars company packages of milk chocolate M&Ms contain 20% orange candies. Suppose we examine 100 random candies. a. What value should we expect for our sample percentage of orange candies? b. What is the standard error? c. Use your answers to fill in the blanks: We expect ____%
Samuel Morse suggested in the nineteenth century that the letter “t” made up 9% of the English language. Assume this is still correct. A random sample of 1000 letters is taken from a randomly selected, large book and the t’s are counted. a. What value should we expect for our sample
A population of college students is taking an advanced math class. In the class are three juniors and two seniors. Using numbers 1, 2, and 3 to represent juniors and 4 and 5 to represent seniors, sample without replacement. Draw a sample of two people four times (once in each of parts a, b, c, and
From a very large (essentially infinite) population, of which half are men and half are women, you take a random sample, with replacement. Use the following random number table and assume each single digit represents selection of one person; the odd numbers represent women and the even numbers (0,
Return to Exercise 7.25 and find the approximate probability that the random sample of 100 will contain 24% or more orange candies.
Return to Exercise 7.26 and find the approximate probability that the random sample of 1000 letters will contain 8.1% or fewer t’s.
Juries should have the same racial distribution as the surrounding communities. According to the U.S. Census, about 18% of residents in Minneapolis, Minnesota, are African American. Suppose a local court randomly selects 100 adult citizens of Minneapolis to participate in the jury pool. Use the
According to an article from HuffingtonPost.com, some experts believe that 20% of all freshwater fish in the United States have such high levels of mercury that they are dangerous to eat. Suppose a fish market has 250 fish we consider randomly sampled from the population of edible freshwater fish.
According to the Oregon Bar Association, approximately 65% of the people who take the bar exam to practice law in Oregon pass the exam. Find the approximate probability that at least 67% of 200 randomly sampled people taking the Oregon bar exam will pass. (In other words, find the probability that
A survey of eating habits showed that approximately 4% of people in Portland, Oregon, are vegans. Vegans do not eat meat, poultry, fish, seafood, eggs, or milk. A restaurant in Portland expects 300 people on opening night, and the chef is deciding on the menu. Treat the patrons as a simple random
The Ventura County Star (June 20, 2012) reported on a study of children in public schools in California that looked at the proportion of overweight or obese children. In Huntington Park (a small city outside Los Angeles), 53% of the children were overweight or obese; this was the highest rate found
The Ventura County Star article mentioned in Exercise 7.41 also reported that 25% of the residents of Huntington Park lived in poverty. Suppose a random sample of 400 residents of Huntington Park is taken. We wish to determine the probability that 30% or more of our sample will be living in
A true/false test has 40 questions. A passing grade is 60% or more correct answers.a. What is the probability that a person will guess correctly on one true/false question?b. What is the probability that a person will guess incorrectly on one question?c. Find the approximate probability that a
A large community college district has 1000 teachers, of whom 50% are men and 50% are women. In this district, administrators are promoted from among the teachers. There are currently 50 administrators, and 70% of these administrators are men.a. If administrators are selected randomly from the
In November 2011, a Pew Poll showed that 1241 out of 2001 randomly polled people in the United States favor the death penalty for those convicted of murder. Assuming the conditions for using the CLT were met, answer these questions.a. Using the Minitab output given, write out the following
When asked whether marriage is becoming obsolete, 782 out of 2004 randomly selected adults who responded to a 2010 Pew Poll said yes. Refer to the output given. Assume the conditions for using the CLT were met.a. Report a 95% confidence interval for the proportion. Use correct wording.b. Is it
According to a Gallup Poll taken in East Germany, when adults were asked whether they were thriving, struggling, or suffering, 261 out of 435 said they were struggling. (The number that said they were suffering was 50. In West Germany the number of those who reported suffering was less than half of
In June 2012, a Gallup Poll asked U.S. adults whether immigration was a good thing or a bad thing for the country. Out of 1004 respondents, 663 said it was a good thing.a. What percentage of those taking the poll said immigration was a good thing?b. Check the conditions to determine whether you can
A random sample of likely voters showed that 55% planned to vote for Candidate X, with a margin of error of 2 percentage points and with a 95% confidence level. a. Use a carefully worded sentence to report the 95% confidence interval for the percentage of voters who plan to vote for Candidate X. b.
A random sample of likely voters showed that 49% planned to support Measure X. The margin of error is 3 percentage points with a 95% confidence level. a. Using a carefully worded sentence, report the 95% confidence interval for the percentage of voters who plan to support Measure X. b. Is there
In a simple random sample of 1500 young Americans, 87% had earned a high school diploma.a. What is the standard error for this estimate of the percentage of all young Americans who earned a high school diploma?b. Find the margin of error, using a 95% confidence level, for estimating the percentage
In a simple random sample of 1200 Americans age 20 and over, the proportion with diabetes was found to be 0.115 (or 11.5%).a. What is the standard error for the estimate of the proportion of all Americans age 20 and over with diabetes?b. Find the margin of error, using a 95% confidence level, for
A 2012 Gallup Poll reported that only 581 out of a total of 2004 U.S. adults said they had a “great deal of confidence” or “quite a lot of confidence” in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met.a.
In June 2012, a Gallup Poll reported that 1503 out of a total of 2004 U.S. adults said they had a “great deal of confidence” or “quite a lot of confidence” in the military. Assume the conditions for using the CLT are met.a. Find a 95% confidence interval for the proportion that reported a
In June 2012, a Gallup Poll showed that when a sample of Americans were asked whether they were thriving, struggling, or suffering, about 54% said they were thriving.a. Assuming the sample size was 1000, how many in the sample said they were thriving?b. Is the sample size large enough to apply the
In May 2012, a Gallup Poll showed that 63% of randomly surveyed U.S. adults said the United States benefits from having a rich class. (The proportion was unchanged from 1990. The percentage was higher for Republicans than for Democrats.)a. Assuming the sample size was 500, how many would have said
Each student in a class of 40 was randomly assigned one line of a random number table. Each student then counted the odd-numbered digits in a 30-digit line. (Remember that 0, 2, 4, 6, and 8 are even.)a. On average, in the list of 30 digits, how many odd-numbered digits would each student find?b. If
Each student in a class of 30 was assigned one random line of a random number table. Each student then counted the even-numbered digits in a 30-digit line.a. On average, in the list of 30 digits, how many even-numbered digits would each student find?b. If each student found an 80% confidence
In the 1960 presidential election, 34,226,731 people voted for Kennedy; 34,108,157 for Nixon; and 197,029 for third-party candidates (www.uselectionatlas.org). a. What percentage of voters chose Kennedy? b. Would it be appropriate to find a confidence interval for the proportion of voters choosing
In a Gallup Poll, 441 of 507 adults said it was “morally wrong” to clone humans.a. What proportion of the respondents believed it morally wrong to clone humans?b. Find a 95% confidence interval for the population proportion who believed it is morally wrong to clone humans. Assume that Gallup
In the 2012 General Social Survey, people were asked their opinions on astrology—whether it was very scientific, somewhat scientific, or not at all scientific. Of 1974 who responded, 101 said astrology was very scientific.a. Find the proportion of people in the survey who believe astrology is
In the 2012 General Social Survey, people were asked whether they thought the sun went around the planet Earth or vice versa. Of 1974 people, 203 thought the sun went around Earth.a. What proportion of people in the survey believed the sun went around Earth?b. Find a 95% confidence interval for the
The Pew Research Center reports on a survey taken in late 2013 in which they asked whether respondents have heard “good news” about the job market. They compared those making $30,000 or less per year with those making between $31,000 and $74,000. We’ll label the population of those making
In a 2013 Pew Poll, 36% of Republicans and 28% of Democrats agreed with the statement “Obesity impacts individuals, but doesn’t have a major impact on society.” A 95% confidence interval for the difference in these proportions is (-0.13 to -0.02), or, in terms of percentage points, (-13% to
An April 2012 Gallup Poll of low-income moms showed that 54% of stay-at-home moms experienced stress, and 49% of employed moms experienced stress. All respondents had an annual household income of less than $36,000.a. Can we conclude, on the basis of these two percentages alone, that in the United
According to the Pew Research Center, 47% of respondents to a poll in April 2012 reported that they strongly favored gay marriage, but in 2004 only 31% said the same thing.a. Can we conclude, from these two percentages alone, that in the United States, a greater percentage favored gay marriage in
The Perry Preschool Project was created in the early 1960s by David Weikart in Ypsilanti, Michigan. In this project, 123 African American children were randomly assigned to one of two groups: One group enrolled in the Perry Preschool, and the other group did not. Follow-up studies were done for
Refer to Exercise 7.67 for information. This data set records results just for the boys.a. Find and compare the percentages that graduated for each group, descriptively. Does this suggest that preschool was linked with a higher graduation rate?b. Verify that the conditions for a two-proportion
A study was done of children from Malawi (in southeastern Africa) with severe acute malnutrition (Trehan et al. 2013). Of the 922 children randomized to receive amoxicillin in addition to food, 817 recovered. Of the 922 children randomized to receive the placebo and food,785 recovered. The trial
Should patients who are bleeding from the stomach get transfusions when their hemoglobin level falls below 7 grams per deciliter (restrictive strategy) or when it falls to 9 grams per deciliter (liberal strategy)? A study used random assignment with 461 patients assigned to the restrictive strategy
Statistics student Hector Porath wanted to find out whether gender and the use of turn signals when driving were independent. He made notes when driving in his truck for several weeks. He noted the gender of each person that he observed and whether he or she used the turn signal when turning or
A randomized, placebo-controlled study of a diet drug (Meridia) was done on overweight or obese subjects and reported in the New England Journal of Medicine (James et al. 2010). The patients were all 55 years old or older with a high risk of cardiovascular events. Those who had a heart event had
Ondansetron (Zofran) is a drug used by some pregnant women for nausea. There was some concern that it might cause trouble with pregnancies. An observational study was done of women in Denmark (Pasternak et al. 2013). An analysis of 1849 exposed women and 7376 unexposed women showed that 2.1% of the
The Perry Preschool Project was created in the early 1960s by David Weikart in Ypsilanti, Michigan. In this project, 123 African American children were randomly assigned to one of two groups: One group enrolled in the Perry Preschool, and one group did not enroll. Follow-up studies were done for
A June 2012 Rasmussen Poll showed that 65% of its randomly selected U.S. adults were opposed to banning super-size sugary soft drinks, with a margin of error of 3 percentage points and a 95% confidence interval. Assume the conditions hold. a. Report the confidence interval for the population
A July 2011 Roper Poll showed that 59% of its randomly selected U.S. adults would support banning smoking in all public places. (This was up from 44% in July 2010.) Suppose the margin of error was 4 percentage points with a 95% confidence interval. Assume the conditions hold for all parts. a.
A poll on a proposition showed that we are 95% confident that the population proportion of voters supporting it is between 40% and 48%. Find the margin of error.
A poll on a proposition showed that we are 99% confident that the population proportion of voters supporting it is between 52% and 62%. Find the margin of error.
Refer to figures (A) and (B) above.a. Compare the percentages of heads in figures (A) and (B).b. Calculate the standard error for the proportion of heads when tossing a fair coin 50 times. Then find the standard error for the proportion of heads when tossing a fair coin 200 times.c. When using the
Refer to figures (A) and (B) on the previous page. When using the CLT for one sample proportion, if you decrease the sample size, the standard error ________________ (increases or decreases), which makes the z-score ___________________________________ (closer to zero or farther from 0), and that
According to studies done in the 1940s, 29% of people dream in color. Assuming this is still true, find the probability that in a random sample of 200 independent people, 50% or more will report dreaming in color. Start by checking the conditions to see whether the Central Limit Theorem applies.
Ignaz Semmelweiss (1818–1865) was the doctor who first encouraged other doctors to wash their hands with disinfectant before touching patients. Before the new procedure was established, the rate of infection at Dr. Semmelweiss’s hospital was about 10%. Afterwards the rate dropped to about 1%.
During the Republican primary elections of 2012, Rasmussen Polls estimated that in Ohio, Mitt Romney would receive 31% of the vote and Rick Santorum would receive 33%. However, Rasmussen claimed that the candidates were in a “statistical tie.” Explain what this means at the level of someone who
In March 2012, President Obama’s approval ratings were the highest they had been in almost a year: 46% of those that Gallup sampled approved of the job Obama was doing as president (www.gallup.com/poll viewed 4/9/12). Gallup reports a margin of sampling error of “plus or minus 1 percentage
Are the career goals of young women changing? A Pew Poll asked young women about the importance they place on having a high-paying career or profession. Those women who said being successful in a high-paying career is €œone of the most important things€ or €œvery important€ in their
Are the career goals of young men changing? A Pew Poll asked young men about the importance they place on having a high-paying career or profession. Those men who said being successful in a high-paying career is “one of the most important things” or “very important” in their lives are

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