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nonparametric statistical inference

Questions and Answers of Nonparametric Statistical Inference

Crickets and Temperature. One classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute. The scatterplot in Figure 7
golf Score/Prize money. Golf scores and prize money won by professional golfers For each pair, state whether you believe the two variables are correlated. If you believe they are correlated, state
height/SaT Score. The heights and SAT scores of randomly selected subjects who take the SAT For each pair, state whether you believe the two variables are correlated. If you believe they are
altitude/Temperature. The outside air temperature and the altitude of aircraft For each pair, state whether you believe the two variables are correlated. If you believe they are correlated, state
Points and DJIa. The total number of points scored in Super Bowl football games and the changes in the Dow Jones Industrial stock index in the years following those games For each pair, state whether
Weight/Fuel Consumption. The total weights of airliners flying from New York to San Francisco and the total amounts of fuel that they consume For each pair, state whether you believe the two
Weight/Fuel Efficiency. The total weights of airliners flying from New York to San Francisco and the fuel efficiency as measured in miles per gallon For each pair, state whether you believe the two
IQ/hat Size. The IQ scores and hat sizes of randomly selected adults For each pair, state whether you believe the two variables are correlated. If you believe they are correlated, state whether the
Weight/Cost. The weights and costs of 50 different bags of apples For each pair, state whether you believe the two variables are correlated. If you believe they are correlated, state whether the
Interpreting r. In investigating correlations between many different pairs of variables, in each case the correlation coefficient r must fall between-1 and 1.decide whether the statement makes sense
Correlation. Two studies both found a correlation between low birth weight and weakened immune systems. The second study had a much larger sample size, so the correlation it found must be
Positive Effect. An engineer for a car company finds that by reducing the weights of various cars, mileage (mi/gal)increases. Because this is a positive result, we say that there is a positive
Births. A study showed that for one town, as the stork population increased, the number of births in the town also increased. It therefore follows that the increase in the stork population caused the
Scatterplot. One set of paired data results in r = 1 and a second set of paired data results in r = -1. How do the corresponding scatterplots differ?
Correlation. After computing the correlation coefficient r from 50 pairs of data, you find that r = 0.Does it follow that there is no relationship between the two variables?Why or why not?
Scatterplot. What is a scatterplot, and how does it help us investigate correlation?
Discuss a few other ways DNA tests can be useful, such as in settling issues of paternity. Overall, how much do you think DNA evidence affects our society?
The Innocence Project uses DNA to try to clear suspects wrongfully convicted of crimes. Is innocence easier to establish than guilt through DNA testing? Explain.
Evidence from blood tests can identify a suspect with a probability of about 1 in 200.Evidence from DNA tests often provides probabilities claimed to be on the order of 1 in 10 million. If you were a
Suppose that an allele has a greater frequency in a suspect’s subpopulation than in the full population, but that the suspect is compared to the full population. How would this affect the
The result of a DNA test is considered physical (as opposed to circumstantial) evidence. Yet it is much more sophisticated and difficult to understand than a typical piece of physical evidence, such
An anonymous quote circulated on the Internet read“Lotteries are a tax on people who are bad at math.”Comment on the meaning and accuracy of this quote.
Considering all factors presented in this section and other facts that you can find, do you think lotteries are fair to poor or uneducated people? Should they remain legal?Should they be restricted
Find and study a particular lottery advertisement, and determine whether it is misleading in any way.
Based on the more than $50 billion in total annual lottery spending and the current U.S. population, about how much does the average person spend on the lottery each year? Now, using the statistics
Study Figure 14.Do lottery players appear to be a typical cross-section of American society based on age? Based on income? Based on level of education?Explain. How does the “no response” category
Find the probability of getting someone who passed, given that the selected person is in Group A.use the following results:In the judicial case of United States v. City of Chicago, discrimination was
Find the probability of randomly selecting one of the test subjects and getting someone who is in Group A and passed the exam.use the following results:In the judicial case of United States v. City
Find the probability of randomly selecting two different test subjects and finding that they are both in Group A.use the following results:In the judicial case of United States v. City of Chicago,
Find the probability of randomly selecting one of the test subjects and getting someone who is in Group B or passed.use the following results:In the judicial case of United States v. City of Chicago,
If one of the test subjects is randomly selected, find the probability of getting someone who passed the exam.use the following results:In the judicial case of United States v. City of Chicago,
If P(A) = 0.4, what is the value of P(A)?
When conducting a clinical trial of the effectiveness of a gender selection method, it is found that there is a 0.342 probability that the results could have occurred by chance.Does the method appear
Estimate the probability that a randomly selected prime-time television show will be interrupted with a news bulletin.
For the same handicapper described in Exercise 1, find the probability that she is correct in each of her next two predictions.
A Las Vegas handicapper can correctly predict the winning professional football team 70% of the time. What is the probability that she is wrong in her next prediction?
For a recent year, the fatality rate from motor vehicle crashes was reported as 15.2 per 100,000 population.a. What is the probability that a randomly selected person will die this year as a result
The Binary Computer Company manufactures computer chips used in DVD players. Those chips are made with a 27% yield, meaning that 27% of them are good and the others are defective.a. If one chip is
Use subjective probability to estimate the probability of randomly selecting a car and selecting one that is black.
If one of the subjects is randomly selected, find the probability of selecting someone who did not wear a helmet, given that the subject had head injuries.use the data in the accompanying table
If two different study subjects are randomly selected, find the probability that they both wore helmets.use the data in the accompanying table (based on data from “Helmet Use and Risk of Head
If one of the subjects is randomly selected, find the probability of selecting someone who did not wear a helmet and was not injured.use the data in the accompanying table (based on data from
If one of the subjects is randomly selected, find the probability of selecting someone who wore a helmet and was injured.use the data in the accompanying table (based on data from “Helmet Use and
If one of the subjects is randomly selected, find the probability of selecting someone who did not wear a helmet or was not injured.use the data in the accompanying table (based on data from
If one of the subjects is randomly selected, find the probability of selecting someone who had a head injury or wore a helmet.use the data in the accompanying table (based on data from “Helmet Use
If one of the subjects is randomly selected, find the probability of selecting someone with a head injury.use the data in the accompanying table (based on data from “Helmet Use and Risk of Head
A columnist for the New York Daily News (Stephen Allensworth) provided tips for selecting numbers in New York State’s lottery. He advocated a system based on the use of “cold digits,” which are
Simulation. A classic probability problem involves a king who wants to increase the proportion of women in his kingdom. He decrees that after a mother gives birth to a son, she is prohibited from
hIV among College Students. Suppose that 3% of the students at a particular college are known to carry HIV.a. If a student has 6 sexual partners during the course of a year, what is the probability
The Bets of the Chevalier de mère. It is said that probability theory was invented in the 17th century to explain the gambling of a nobleman named the Chevalier de Mère.a. In his first game, the
BINgo. The game of BINGO involves drawing numbered and lettered buttons at random from a barrel. The B numbers are 1–15, the I numbers are 16–30, the N numbers are 31–45, the G numbers are
Probability Distributions and genetics. Many traits are controlled by a dominant gene, denoted bya, and a recessive gene, denoted bya. Suppose that two parents carry these genes in the proportion
Survey Refusals. Refer to the following table summarizing results from a study of people who refused to answer survey questions (based on data from “I Hear You Knocking but You Can’t Come In,”
Drug Tests. An allergy drug is tested by giving 120 people the drug and 100 people a placebo. A control group consists of 80 people who were given no treatment. The number of people in each group who
If two different pedestrian deaths are randomly selected, find the probability that in both cases the pedestrians were intoxicated.use the following table, which summarizes data on 985 pedestrian
If two different pedestrian deaths are randomly selected, find the probability that they both involved intoxicated drivers.use the following table, which summarizes data on 985 pedestrian deaths that
If one of the pedestrian deaths is randomly selected, find the probability that the driver was intoxicated or the pedestrian was not intoxicated.use the following table, which summarizes data on 985
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was not intoxicated.use the following table, which summarizes data on 985
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.use the following table, which summarizes data on
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated.use the following table, which summarizes data on 985
If a defendant is randomly selected, what is the probability that the defendant entered a guilty plea and was not sent to prison?The data in the following table show the outcomes of guilty and
If a defendant is randomly selected, what is the probability that the defendant entered a guilty plea and was sent to prison?The data in the following table show the outcomes of guilty and not-guilty
If two different defendants are randomly selected, what is the probability that they both were sentenced to prison?The data in the following table show the outcomes of guilty and not-guilty pleas in
If two different defendants are randomly selected, what is the probability that they both entered guilty pleas?The data in the following table show the outcomes of guilty and not-guilty pleas in
What is the probability that a randomly selected defendant either pled not guilty or was not sent to prison?The data in the following table show the outcomes of guilty and not-guilty pleas in 1,028
What is the probability that a randomly selected defendant either pled guilty or was sent to prison?The data in the following table show the outcomes of guilty and not-guilty pleas in 1,028 criminal
Polling Calls. A telephone pollster has names and telephone numbers for 45 voters, 20 of whom are registered Democrats and 25 of whom are registered Republicans.Calls are made in random order.
Radio Tunes. An MP3 player is loaded with 60 musical selections: 30 rock selections, 15 jazz selections, and 15 blues selections. The player is set on “random play,” so selections are played
Wearing hunter orange. A study of hunting injuries and the wearing of hunter orange clothing showed that among 123 hunters injured when mistaken for game, 6 were wearing orange (based on data from
Password. A new computer owner creates a password consisting of five characters. She randomly selects a letter of the alphabet for the first character and a digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) for
Births. A couple plans to have four children. Find the probability that the first two children are girls and the last two children are boys.
Births. Assume that boys and girls are equally likely and that the gender of a child is independent of the gender of any brothers or sisters. If a couple already has three girls, find the probability
Lottery. The probability of your winning the state lottery this week is not affected by whether you won that same lottery last week.decide whether the statement makes sense (or is clearly true) or
Either/Or Probability. P(A) = 0.5 and P(A or B) = 0.8.decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these
Combining Probabilities. The probability of flipping a coin and getting heads is 0.5. The probability of selecting a red card when one card is drawn from a shuffled deck is also 0.5. When flipping a
Lottery. The numbers 5, 17, 18, 27, 36, and 41 were drawn in the last lottery; they should not be bet on in the next lottery because they are now less likely to occur.decide whether the statement
Complementary Events. Let A denote some event. Are events A and A non-overlapping? Why or why not?
Sampling with Replacement? The professor in a class of 25 students randomly selects a student and then randomly selects a second student. If all 25 students are available for the second selection, is
Non-overlapping Events. In your own words, state what it means for two events to be non-overlapping.
Independence. Let A denote the event of turning on your cell phone and finding that it works, and let B denote the event of turning on your car radio and finding that it works. Are events A and B
Vital Statistics. Find a recent news report that gives current data about vital statistics or life expectancy. Summarize the report and the statistics, and discuss any personal or social implications
Travel Safety. Find a recent news article discussing some aspect of travel safety (such as risk of accidents in automobiles or airplanes, the efficacy of child car seats, or the effects of driving
understanding Risk. The book Against the Gods: The Remarkable Story of Risk by Peter Bernstein (John Wiley, 1996) is an award-winning account of the history of probability and risk assessment. Find
Richter Scale for Risk. The Royal Statistical Society has proposed a system of risk magnitudes and risk factors analogous to the Richter scale for measuring earthquakes.Go to the Internet to learn
Life Expectancy Calculations. You will find many life expectancy calculators available on the Internet; try a few of them. Do they seem to give accurate or realistic results?Explore the statistical
uganda Case Study. Find data regarding life expectancies in Uganda over the past few decades. You will see that Ugandan life expectancy has risen dramatically in the past decade. What explains this
male and Female Life Expectancies. Find data about how and why male and female life expectancies are changing with time. Why do women have longer life expectancies than men? Should we expect male
u.S. vs. World Life Expectancy. You can find a great deal of data on the Web about life expectancies around the world. How does U.S. life expectancy compare to life expectancy in other developed
China Birth and Death Rates. These estimated 2011 values are for China: population = 1,336,718,015; birth rate =12.3 per 1,000; death rate = 7.0 per 1,000.a. Approximately how many births were there
u.S. Birth and Death Rates. In 2011, the estimated U.S.population reached 313 million. The overall birth rate was estimated to be 13.8 births per 1,000, and the overall death rate was estimated to be
high/Low u.S. Death Numbers. In a recent year, there were 235,000 deaths in California, the highest number in the United States. The state with the lowest number of deaths was Alaska, with 3,000
high/Low u.S. Birth Rates. The highest and lowest birth rates in the United States in 2008 were in Utah and Maine, respectively. Utah reported 55,633 births with a population of 2,736,424 people.
Death Rate. Find the death rate per 10,000 for people during their 17th year (age 16–17).use the data in the following table for people in the United States between the ages of 16 and 21 years.
Death Rate. Life insurance companies must carefully monitor death rates. Before issuing a life insurance policy for a 19-year-old, the company needs to know the death rate for that age group. Find
Expected Lifetime. How many years is a randomly selected 17-year-old expected to live beyond his or her 17th birthday?use the data in the following table for people in the United States between the
Expected Lifetime. How many years is a randomly selected 19-year-old expected to live beyond his or her 19th birthday?use the data in the following table for people in the United States between the
For the year 2008, find the fatality rate in deaths per passenger mile. Why don’t we report the fatality rate in units of deaths per passenger mile?use the following table, which summarizes data on
For each of the three years, find the fatality rate in deaths per million passengers. On the basis of those rates, which year was the safest? Why?use the following table, which summarizes data on
For each of the three years, find the fatality rate in deaths per billion passenger miles. On the basis of those rates, which year was the safest? Why?use the following table, which summarizes data
For each of the three years, find the fatality rate in deaths per 1,000 departures. On the basis of those rates, which year was the safest? Why?use the following table, which summarizes data on

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