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nonparametric statistical inference

Questions and Answers of Nonparametric Statistical Inference

Risk of Death. In a recent year, the total numbers of deaths in the United States due to either accidents or pneumonia were approximately decide whether the statement makes sense (or is clearly true)
Expected age at Death. As you become older, your expected age at death increases.decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain
Life Expectancy. Your life expectancy increases as your age increases.decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. Not
Life Expectancy. Because people are not expected to live longer than 90 years, a 100-year-old person has a negative life expectancy.decide whether the statement makes sense (or is clearly true) or
Life Expectancy. Based on recent data, a 20-year-old person in the United States has a life expectancy of 58.8 years.What does that mean?
Life Expectancy. What is life expectancy? Does a 30-yearold person have the same life expectancy as a 20-year-old person? Why or why not?
Vital Statistics. What are vital statistics?
Birth Rate. The current U.S. birth rate is given as 13.5 per 1,000 population. When comparing population growth in different countries, why is it better to use birth rates instead of the actual
gambler’s Ruin. Describe a situation you know of in which someone lost nearly everything through gambling. Did his or her strategy appear to be rational, or did it appear to be the result of a
gambler’s Fallacy in Life. Describe a situation in which you or someone you know has fallen victim to the gambler’s fallacy. How could the situation have been dealt with correctly?
Personal Law of Large Numbers. Describe a situation in which you personally have made use of the law of large numbers, either correctly or incorrectly. Why did you use the law of large numbers in
Law of Large Numbers. Use a coin to simulate 100 births: Flip the coin 100 times, recording the results, and then convert the outcomes to genders of babies(tail = boy and head = girl). Use the
analyzing Lotteries on the Web. Go to the Web site for all U.S. lotteries and study the summary of state and multistate lottery odds and prizes. Pick five lotteries and determine the expected value
Behind in Coin Tossing: Can you Catch up? Suppose that you toss a fair coin 100 times, getting 38 heads and 62 tails, which is 24 more tails than heads.a. Explain why, on your next toss, the
gambler’s Fallacy and Dice. Suppose you roll a die with a friend, with the following rules: For every even number you roll, you win $1 from your friend; for every odd number you roll, you pay $1 to
Expected Value for a magazine Sweepstakes. Reader’s Digest ran a sweepstakes in which prizes were listed along with the chances of winning: $1,000,000 (1 chance in 90,000,000), $100,000 (1 chance
Psychology of Expected Values. In 1953, a French economist named Maurice Allais conducted a survey of how people assess risk. Here are two scenarios that he used, each of which required people to
New Jersey Pick 4.In New Jersey’s Pick 4 lottery game, you pay 50¢ to select a sequence of four digits, such as 2273, from the 10,000 different possible four-digit sequences. If you select the
Expected Value in Casino Dice. When you give a casino$5 for a bet on the “pass line” in a casino game of dice,there is a 251/495 probability that you will lose $5 and there is a 244/495
Expected Value in Roulette. When you give the Venetian casino in Las Vegas $5 for a bet on the number 7 in roulette, you have a 37/38 probability of losing $5 and you have a 1/38 probability of
Big game. The Multi-State Big Game lottery advertises the following prizes and probabilities of winning for a single $1 ticket. The jackpot is variable, but assume it has an average value of $3
Powerball Lottery. The multi-state Powerball lottery advertises the following prizes and probabilities of winning for a single $1 ticket. Assume the jackpot has a value of$30 million one week. Note
Expected Waiting Time. Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. The bus arrives regularly every 30 minutes without delay (say, on the hour and on the
Insurance Claims. An actuary at an insurance company estimates from existing data that on a $1,000 policy, an average of 1 in 100 policyholders will file a $20,000 claim, an average of 1 in 200
Extra Points in Football. Football teams have the option of trying to score either 1 or 2 extra points after a touchdown. They get 1 point by kicking the ball through the goal posts or 2 points by
Kentucky’s Pick 4 Lottery. If you bet $1 in Kentucky’s Pick 4 lottery game, you either lose $1 or gain $4,999. (The winning prize is$5,000, but your $1 bet is not returned, so the net gain is
Should you Play? Suppose someone offers you this opportunity:You can place a bet of $10 and roll a single die once. You win twice the outcome of the die. For example, if you roll a 6, you win $12 for
Speedy Driver. A person who has a habit of driving fast has never had an accident or traffic citation. What does it mean to say that “the law of averages will catch up with him”? Is it true?
gender Selection. In planning an experiment designed to test the effectiveness of a gender selection method, assume that boys and girls are equally likely to be born. Among 500 births, should we
Lottery. Jennifer purchases a state lottery ticket and she avoids the combination of 1, 2, 3, 4, 5, and 6.She reasons that this combination has the same chance as any other combination, but the
Lottery. When considering the chances of winning a lottery, Kim reasons that the number combination of 1, 2, 3, 4, 5, and 6 is less likely to occur because of the obvious pattern.decide whether the
Lottery. Kelly studies the Wisconsin Pick 3 lottery and finds that for a $1 bet, the expected return is 50¢, so she reasons that this is bad bet and she does not play.decide whether the statement
Gambling Strategy. Steve learns that for a $5 bet on a number in roulette, the expected return is $4.74, but for a$5 bet on the pass line in the game of craps, the expected return is $4.93, so it is
Gambler’s Fallacy. In your own words, describe the gambler’s fallacy.
Gambling Strategy. A professional gambler playing blackjack in the Venetian casino has lost each of his first 10 bets.He begins to place larger bets, reasoning that his current proportion of wins
Expected Value. A geneticist computes the expected number of girls in 5 births and obtains the result of 2.5 girls. He rounds the result to 3 girls, reasoning that it is impossible to get 2.5 girls
Law of Large Numbers. In your own words, describe the law of large numbers.
Probability Distributions. Find a news article or research report that cites or makes use of a probability distribution. Provide a one-paragraph discussion.
Subjective Probabilities. Find a news article or research report that refers to a subjective probability.Provide a one-paragraph discussion.
Relative Frequency Probabilities. Find a news article or research report that makes use of a relative frequency (or empirical) probability. Provide a oneparagraph discussion.
Theoretical Probabilities. Find a news article or research report that cites a theoretical probability.Provide a one-paragraph discussion.
Randomizing a Survey. Suppose you want to conduct a survey involving a sensitive question that not all participants may choose to answer honestly (for example, a question involving cheating on taxes
Three-Coin Experiment. Toss three coins at once 50 times and record the outcomes in terms of the number of heads. Based on your observations, give the relative frequency probabilities of the
Thumb Tack Probabilities. Find a standard thumb tack and practice tossing it onto a flat surface. Notice that there are two different outcomes: The tack can land point down or point up.a. Toss the
age and gender. The proportions of men and women in the population change with age. Using current data from a Web site, construct a table showing the probability of meeting a male or a female in each
Blood groups. The four major blood groups are designated A, B, AB, and O. Within each group there are two Rh types: positive and negative. Using library resources or the Internet, find data on the
Colorado Lottery Distribution. The histogram in Figure 7 shows the distribution of 5,964 Colorado lottery numbers(possible values range from 1 to 42).a. Assuming the lottery drawings are random, what
Four-Coin Probability Distribution.a. Construct a table similar to Table 2, showing all possible outcomes of tossing four coins at once.b. Construct a table similar to Table 3, showing the
age at First marriage. The following table gives percentages of women and men married for the first time in several age categories (U.S. Census Bureau)a. What is the probability that a randomly
Senior Citizen Probabilities. In the year 2000, there were 34.7 million people over 65 years of age out of a U.S. population of 281 million. In the year 2050, it is estimated that there will be 78.9
Surgery. In a clinical trial of 73 carpal tunnel syndrome patients treated with surgery, 67 had successful treatments(based on data from “Splinting vs. Surgery in the Treatment of Carpal Tunnel
Basketball. Halfway through the season, a basketball player has hit 86% of her free throws. What is the probability that her next free throw will be successful?Use the relative frequency method to
Flood. What is the probability of a 100-year flood this year?Use the relative frequency method to estimate the probabilities.
Weather Forecast. After recording the forecasts of your local weatherman for 30 days, you conclude that he gave a correct forecast 18 times. What is the probability that his next forecast will be
Four-Child Family. Suppose you randomly select a family with four children. Assume that births of boys and girls are equally likely.a. How many birth orders are possible? List all of them.b. What is
Three-Child Family. Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely. What is the probability that the family has each of the
Test Questions. The New England College of Medicine uses an admissions test with multiple-choice questions, each with five possible answers, only one of which is correct. If you guess randomly on
m&ms. A bag contains 10 red M&Ms, 15 blue M&Ms, and 20 yellow M&Ms. What is the probability of drawing a red M&M? A blue M&M? A yellow M&M? Something besides a yellow M&M?use the theoretical method
Defects. What is the probability of not getting a defective fuse when one fuse is randomly selected from an assembly line and 1% of the fuses are defective?find the probability of the given event.
Baseball. What is the probability that a 0.280 hitter in baseball will not get a hit on his next at-bat?find the probability of the given event. State any assumptions that you use.
Testing. What is the probability of guessing incorrectly when making a random guess on a multiple-choice test question with possible answers ofa, b,c, d, ande, one of which is correct?
Basketball. What is the probability that a 55% free-throw shooter will miss her next free throw?find the probability of the given event. State any assumptions that you use.
Birthday. What is the probability of finding that the next President of the United States was not born on Saturday?find the probability of the given event. State any assumptions that you use.
Week Days. What is the probability of randomly selecting a day of the week and not getting Monday?find the probability of the given event. State any assumptions that you use.
Die. What is the probability of rolling a fair die and not getting an outcome that is greater than 6?find the probability of the given event. State any assumptions that you use.
Die. What is the probability of rolling a fair die and not getting an outcome less than 7?find the probability of the given event. State any assumptions that you use.
Dice. Rolling a pair of dice and getting an outcome (sum)of 12.use the theoretical method to determine the probability of the given outcome or event. State any assumptions that you need to make.
Births. Finding that the next baby born to a couple is a girl, given that the couple already has two children and they are both boys.use the theoretical method to determine the probability of the
Births. Finding that the next baby born in Alaska is a girl.use the theoretical method to determine the probability of the given outcome or event. State any assumptions that you need to make.
Birthday. Finding that the next person you meet has the same birthday as yours (Ignore leap years.).use the theoretical method to determine the probability of the given outcome or event. State any
Birthday. Finding that the next President of the United States was born on Saturday.use the theoretical method to determine the probability of the given outcome or event. State any assumptions that
Roulette. Getting an outcome of a red slot when a roulette wheel is spun (A roulette wheel has slots of 0, 00, 1, 2, 3, . . . , 36, and 18 of those slots are red.).use the theoretical method to
Test Question. Making a correct random guess for an answer to a particular multiple-choice question with possible answers ofa, b,c, d,e, one of which is correct.use the theoretical method to
Die. Rolling a die and getting an outcome that is greater than 2.use the theoretical method to determine the probability of the given outcome or event. State any assumptions that you need to make.
Lightning. Jill estimates that the subjective probability of her being struck by lightning sometime next year is 1/1,000,000.decide whether the statement makes sense (or is clearly true) or does not
Lightning. Jack estimates that the subjective probability of his being struck by lightning sometime next year is 1/2.decide whether the statement makes sense (or is clearly true) or does not make
Car Crash. An insurance company states that the probability that a particular car will be involved in a car crash this year is 0.6 and the probability that the car will not be involved in a car crash
Complementary Events. If there is a 0.9 probability that it will rain sometime today, then there is a probability of 0.1 that it will not rain sometime today.decide whether the statement makes sense
Impossible Event. Because it is impossible for Thanksgiving to fall on Tuesday, the probability of Thanksgiving falling on Tuesday is 0.decide whether the statement makes sense (or is clearly true)
Certain Event. When randomly selecting a day of the week, it is certain that you will select a day containing the letter y, so P(y) = 1.decide whether the statement makes sense (or is clearly true)
Subjective Probability. Use subjective judgment to estimate the probability that the next time you ride an elevator, it gets stuck between floors.
Interpreting Probability. What do we mean when we say that “the probability of getting 20 babies of the same gender when 20 random babies are born is 1/524,288? Is such an event unusual? Why or why
Probability of Life. A student reasons that there is a probability of 1/2 that there is life on Neptune, because there are two possible events: There is life or there is not life. Is this reasoning
Notation. If A denotes the event that you answer a particular true/false test question correctly, what do each of the following represent: P(A), P(not A), P(A), and what are their values?
Personal Statistical Significance. Describe an incident in your own life that did not meet your expectation, defied the odds, or seemed unlikely to have occurred by chance. Would you call this
Significant Experiment? Find a recent news story about a statistical study that used an experiment to determine whether some new treatment was effective.Based on the available information, briefly
Statistical Significance. Find a recent newspaper article on a statistical study in which the idea of statistical significance is used. Write a one-page summary of the study and the result that is
Lengths of Rivers. Using an almanac or the Internet, find the lengths of the principal rivers of the world. Construct a list of the leading digits only. Does any particular digit occur more often
Significance in Vital Statistics. Visit a Web site that has vital statistics (for example, the U.S. Census Bureau or the National Center for Health Statistics). Choose a question such as one of the
Weight by age. A National Health Survey determined that the mean weight of a sample of 804 men ages 25 to 34 years was 176 pounds, while the mean weight of a sample of 1,657 men ages 65 to 74 years
SaT Preparation. A study of 75 students who took an SAT preparation course (American Education Research Journal, Vol. 19, No. 3) concluded that the mean improvement on the SAT was 0.6 point. If we
Seat Belts and Children. In a study of children injured in automobile crashes (American Journal of Public Health, Vol. 82, No. 3), those wearing seat belts had a mean stay of 0.83 day in an intensive
human Body Temperature. In a study by researchers at the University of Maryland, the body temperatures of 106 individuals were measured; the mean for the sample was 98.20°F. It is commonly believed
Bednets and malaria. In a randomized controlled trial in Kenya, insecticide-treated bednets were tested as a way to reduce malaria. Among 343 infants who used the bednets, 15 developed malaria. Among
gender Selection. The Genetics and IVF Institute conducted a clinical trial of its method for gender selection.The latest actual results showed that among 945 babies born to couples using the XSORT
Carpal Tunnel Syndrome Treatments. An experiment was conducted to determine whether there is a difference between the success rates from treating carpal tunnel syndrome with surgery and with
Fuel Tests. Thirty identical cars are selected for a fuel test. Half of the cars are filled with regular gasoline, and the other half are filled with a new experimental fuel. The cars in the first
Clinical Trial. In a clinical trial of a new drug intended to treat allergies, 5 of the 80 subjects in the treatment group experienced headaches, and 8 of the 160 subjects in the control group
Jury Composition. For a trial on a charge of failure to pay child support, the jury consists of exactly 6 men and 6 women.state whether the difference between what occurred and what you would have
Subway Riders. A commuter enters a New York City subway car near Times Square and finds that it is occupied by 50 men, all of whom are bald.state whether the difference between what occurred and what

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