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nonparametric statistical inference

Questions and Answers of Nonparametric Statistical Inference

bMI for Miss America. The trend of thinner Miss America winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for
It’s raining cats. Statistics are sometimes used to compare or identify authors of different works. The lengths of the first 20 words in the foreword by Tennessee Williams in Cat on a Hot Tin Roof
Quarters. Weights (in grams) of quarters in circulation:5.60 5.63 5.58 5.56 5.66 5.58 5.57 5.59 5.67 5.61 5.84 5.73 5.53 5.58 5.52 5.65 5.57 5.71 5.59 5.53 5.63 5.68 each list a set of numbers. In
Weights of M&Ms. Weights (in grams) of randomly selected M&M plain candies:0.957 0.912 0.842 0.925 0.939 0.886 0.914 0.913 0.958 0.947 0.920 each list a set of numbers. In each case, find the range
old Faithful geyser. Time intervals (in minutes)between eruptions of Old Faithful geyser in Yellowstone National Park:98 92 95 87 96 90 65 92 95 93 98 94 each list a set of numbers. In each case,
blood Alcohol. Blood alcohol concentrations of drivers involved in fatal crashes and then given jail sentences (based on data from the U.S. Department of Justice):0.27 0.17 0.17 0.16 0.13 0.24 0.29
body Temperatures. Body temperatures (in degrees Fahrenheit) of randomly selected normal and healthy adults:98.6 98.6 98.0 98.0 99.0 98.4 98.4 98.4 98.4 98.6 each list a set of numbers. In each case,
Perception of Time. Actual times(in seconds) recorded when statistics students participated in an experiment to test their ability to determine when one minute (60 seconds)had passed:53 52 75 62 68
Space Shuttle Flights. Listed below are the durations (in hours) of a sample of all flights of NASA’s Space Transport System (space shuttle):73 95 235 192 165 262 191 376 259 235 381 331 221 244 0
Number of Words. Pages from Merriam-Webster’s Collegiate Dictionary, 11th edition, were randomly selected.Here are the numbers of words defined on those pages:51 63 36 43 34 62 73 39 53 79 each
baseball Salaries. If the range of salaries paid to baseball players in the American League is less than the range of salaries paid to baseball players in the National League, then the American
baseball Salaries. For a recent year, the 817 salaries paid to professional baseball players have a median of$1,152,000 and a second quartile with the same value of$1,152,000.decide whether the
lengths. The house key lengths of 15 statistics students are measured and rounded to the nearest centimeter, and all 15 values are the same, so the standard deviation is 0 cm.decide whether the
SAT Score. Jennifer received an SAT score that was equal to the first quartile and the 35th percentile.decide whether the statement makes sense (or is clearly true) or does not make sense (or is
Quartiles. For the salaries paid to the 817 professional baseball players in a recent year, the first quartile is $4,355,101.What do we mean when we say that $4,355,101 is the first quartile?
correct Statement? In the book How to Lie with Charts, the author writes that “the standard deviation is usually shown as plus or minus the difference between the high and the mean, and the low and
Standard Deviation. Assume that you are manufacturing aspirin tablets that are supposed to contain 325 mg of aspirin. If the standard deviation of the amounts of aspirin is calculated, which value
range. How is the range computed for a set of sample data? Is the range a measure of variation? What is a major disadvantage of the range?
Skewed Distribution. Give an example of a real distribution that you would expect to be either right- or left-skewed. Make a rough sketch of the distribution;be sure to label the axes on your sketch.
Trimodal Distribution. Give an example of a real distribution that you expect to have three modes. Make a rough sketch of the distribution; be sure to label the axes on your sketch.
Distributions in the News. Find three recent examples in the news of distributions shown as histograms or line charts. Over each distribution, draw a smooth curve that captures its general features.
Social Security Data. Survey a sample of fellow students, asking each to indicate the last digit of her or his Social Security number. Also ask each participant to indicate the fifth digit. Draw one
Tax Stats. The IRS Web site provides statistics collected from tax returns on income, refunds, and much more.Choose a set of statistics from this Web site and study the distribution. Describe the
New york Marathon. The Web site for the New York City marathon gives frequency data for finish times in the most recent marathon. Study the data, make a rough sketch of the distribution, and describe
Times. The amounts of time that 5000 randomly selected individual taxpayers used to prepare their federal tax returns answer the following questions:a. How many modes would you expect for the
Incomes. The incomes of people sitting in luxury boxes at the Super Bowl answer the following questions:a. How many modes would you expect for the distribution?b. Would you expect the distribution to
Patron Ages. The ages of people who visit Disneyworld answer the following questions:a. How many modes would you expect for the distribution?b. Would you expect the distribution to be symmetric,
Patron Ages. The ages of adults who visit the National Air and Space Museum answer the following questions:a. How many modes would you expect for the distribution?b. Would you expect the distribution
Speeds. The speeds of drivers on a highway in Montana answer the following questions:a. How many modes would you expect for the distribution?b. Would you expect the distribution to be symmetric,
Patients. The ages of 1,000 randomly selected patients being treated for dementia answer the following questions:a. How many modes would you expect for the distribution?b. Would you expect the
Vehicle Weights. The weights of cars in a fleet consisting of 50 compact cars and 50 delivery trucks answer the following questions:a. How many modes would you expect for the distribution?b. Would
Weights of cola. The weights of the cola in 1000 randomly selected cans of Coke answer the following questions:a. How many modes would you expect for the distribution?b. Would you expect the
heights. The heights of 500 male students, half of whom are adults while the other half are eight years of age answer the following questions:a. How many modes would you expect for the
heights. The heights of 250 randomly selected male attorneys answer the following questions:a. How many modes would you expect for the distribution?b. Would you expect the distribution to be
reaction Times. The reaction times of 500 randomly selected drivers, measured under standard conditions answer the following questions:a. How many modes would you expect for the distribution?b. Would
Incomes. The annual incomes of all those in a statistics class, including the instructor answer the following questions:a. How many modes would you expect for the distribution?b. Would you expect the
boston rainfall. The daily rainfall amounts (in inches) for Boston in a recent year consist of 365 values with these properties:• The mean daily rainfall amount is 0.083 inch.• The median of the
baseball Salaries. In a recent year, the 817 professional baseball players had salaries with the following characteristics:• The mean was $3,250,178.• The median was $1,152,000.• The salaries
Penny Weights. The histogram in Figure 12 shows the weights (in grams) of 72 pennies. Over the histogram, draw a smooth curve that captures its general features. Then classify the distribution
rugby Weights. The histogram in Figure 11 shows the weights of a sample of 391 rugby players. Over the histogram, draw a smooth curve that captures its general features. Then classify the
chip Failures. The histogram in Figure 10 shows the time until failure for a sample of 108 computer chips. Over the histogram, draw a smooth curve that captures its general features. Then classify
old Faithful. The histogram in Figure 9 shows the times between eruptions of Old Faithful geyser in Yellowstone National Park for a sample of 300 eruptions (with 299 times between eruptions). Over
uniform Distribution. Examination of a data set reveals that the mean and median are both equal to 98.2, so the distribution must be uniform.decide whether the statement makes sense (or is clearly
Distribution. Examination of a data set reveals that its distribution is left-skewed and unimodal.decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly
Symmetry. Examination of the data set reveals that it is symmetric with a mean of 98.2 and a median of 98.2.decide whether the statement makes sense (or is clearly true) or does not make sense (or is
Symmetry. Because a data set has three modes, it must have a skewed distribution.decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain
Skewness. What is skewness in a graph?
IQ Scores. Consider the IQ scores of professors who teach statistics courses compared with the IQ scores of adults randomly selected from the general population. Which of these two sets of IQ scores
Distribution. When the digits 0 through 9 are selected for a state lottery, the digits are selected in a way that they are all equally likely. Which term best describes the distribution of selected
Symmetry. In the United States, there are many people with little or no accumulated wealth, and there are a few people with very large amounts of wealth. What does this suggest about the symmetry of
Averages in the News. Find three recent news articles that refer to some type of average. In each case, explain whether the average is a mean, a median, or some other type of average.
Daily Averages. Cite three examples of averages that you deal with in your own life (such as grade point average or batting average). In each case, explain whether the average is a mean, a median, or
Navel Data. The navel ratio is defined to be a person’s height divided by the height (from the floor) of his or her navel. Measure the navel ratio of each person in your class and bin the data.
Is the Median the Message? Read the article “The Median Isn’t the Message,” by Stephen Jay Gould, which is posted on the Web. Write a few paragraphs in which you describe the message that Gould
Salary Data. Many Web sites offer data on salaries in different careers. Find salary data for a career you are considering. What are the mean and median salaries for this career? How do these
u.S. Population center. Imagine taking a huge flat map of the United States and placing weights on it to represent where people live. The point at which the map would balance is called the mean
Phenotypes of Peas. An experiment was conducted to determine whether a deficiency of carbon dioxide in soil affects the phenotypes of peas. Listed below are the phenotype codes, where 1 = smooth
gPA. One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who
Stockholder Voting. A small company has four stockholders. One stockholder has 400 shares, a second stockholder has 300 shares, a third stockholder has 200 shares, and the fourth stockholder has 100
Slugging Average. In addition to the batting average, another measure of hitting performance in baseball is called the slugging average. In finding a slugging average, a single is worth 1 point, a
batteries. A manufacturer uses two different production sites to make batteries for cell phones. There is a defect rate of 2%at one of the sites, and the defect rate at the other site is 4%.Does it
Averaging Averages. Suppose a player has a batting average over many games of 0.200 (he’s not very good). In his next game, he goes 2 for 4, which is a batting average of 0.500 for the game. Does
batting Average. A batting average in baseball is determined by dividing the total number of hits by the total number of at-bats (neglecting walks, sacrifices, and a few other special cases). A
Final grade. Your course grade is based on one midterm that counts as 15% of your final grade, one class project that counts as 20% of your final grade, a set of homework assignments that counts as
Different Means? Each of the 300 students at a high school takes the same four courses. Three of the courses are each taught in 15 classes of 20 students each. The fourth course is taught in 3
Average confusion. An instructor has a first-period class with 25 students, and they had a mean score of 86% on the midterm exam. The second-period class has 30 students, and they had a mean score of
Average Peaches. A grocer has three baskets of peaches.One holds 50 peaches and weighs 18 pounds, one holds 55 peaches and weighs 22 pounds, and the third holds 60 peaches and weighs 24 pounds. What
comparing Averages. Suppose the National Basketball Association (NBA) reports that the average height of basketball players is 6’8”. As a coach, you know that the players on your starting lineup
comparing Averages. Suppose that school district officials claim that the average reading score for fourth-graders in the district is 73 (out of a possible 100). As a principal, you know that your
raising your grade. Suppose you have scores of 60, 70, 65, 85, and 85 on exams in a sociology class.a. What is the mean of these scores?b. What score would you need on the next exam to have an
raising your grade. Suppose you have scores of 80, 84, 87, and 89 on quizzes in a mathematics class.a. What is the mean of these scores?b. What score would you need on the next quiz to have an
outlier coke. Cans of regular Coca-Cola vary slightly in weight. Here are the measured weights of seven cans, in pounds:0.8161 0.8194 0.8165 0.8176 0.7901 0.8143 0.8126a. Find the mean and median of
Alphabetic States. The following table gives the total area in square miles (land and water) of the seven states with names beginning with the letters A through C.a. Find the mean area and median
Quarters. Weights (in grams) of quarters in circulation:5.60 5.63 5.58 5.56 5.66 5.58 5.57 5.59 5.67 5.61 5.84 5.73 5.53 5.58 5.52 5.65 5.57 5.71 5.59 5.53 5.63 5.68 each list a set of numbers. In
Weights of M&Ms. Weights (in grams) of randomly selected M&M plain candies:0.957 0.912 0.842 0.925 0.939 0.886 0.914 0.913 0.958 0.947 0.920 each list a set of numbers. In each case, find the mean,
old Faithful geyser. Time intervals (in minutes) between eruptions of Old Faithful geyser in Yellowstone National Park:98 92 95 87 96 90 65 92 95 93 98 94 each list a set of numbers. In each case,
blood Alcohol. Blood alcohol concentrations of drivers involved in fatal crashes and then given jail sentences(based on data from the U.S. Department of Justice):0.27 0.17 0.17 0.16 0.13 0.24 0.29
body Temperatures. Body temperatures (in degrees Fahrenheit) of randomly selected normal and healthy adults:98.6 98.6 98.0 98.0 99.0 98.4 98.4 98.4 98.4 98.6 each list a set of numbers. In each case,
Perception of Time. Actual times (in seconds) recorded when statistics students participated in an experiment to test their ability to determine when one minute (60 seconds) had passed:53 52 75 62 68
Space Shuttle Flights. Listed below are the durations (in hours) of a sample of all flights of NASA’s Space Transport System (space shuttle):73 95 235 192 165 262 191 376 259 235 381 331 221 244 0
Number of Words. Pages from Merriam-Webster’s Collegiate Dictionary, 11th edition, were randomly selected.Here are the numbers of words defined on those pages:51 63 36 43 34 62 73 39 53 79 each
Pulse rates. The average resting pulse rate of 500 randomly selected female statistics students list “averages” that someone might want to know. In each case, state whether the mean or median
Ages. The following ages (years) of survey respondents: 22, 19, 21, 27, “over 65,” “over 80”list “averages” that someone might want to know. In each case, state whether the mean or median
Salary. The average salary of all active professional basketball players list “averages” that someone might want to know. In each case, state whether the mean or median would give a better
height. The average height of all active professional basketball players list “averages” that someone might want to know. In each case, state whether the mean or median would give a better
Weighted Mean. A professor calculates final grades using a weighted mean in which the final exam counts twice as much as the midterm.decide whether the statement makes sense (or is clearly true) or
Mean, Median, and Mode. A researcher studying an income distribution obtains the same value of $75,000 for the mean, median, and mode.decide whether the statement makes sense (or is clearly true) or
Mode. A data set of incomes has modes of $50,000 and$80,000.decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of
Mean. The number on the jersey of each New York Giants football player is recorded, then the mean of those numbers is computed.decide whether the statement makes sense (or is clearly true) or does
Is the result the mean income for the United States? Why or why not?
Mean Income. An economist wants to find the mean annual income for all adults in the United States. She knows that it is not practical to survey each member of the adult population, so she refers to
outlier. For the same statistics class described in Exercise 2, is the executive secretary’s salary an outlier? Why or why not? In general, is an outlier defined in an exact way so that it can be
Mean and Median. A statistics class consists of 24 students, all but one of whom are unemployed or are employed in low-paying part-time jobs. One student works as an executive secretary earning
Average and Mean. Do the terms “average” and “mean”have the same meaning? Explain.
The graphs in Figure 46 summarize a great deal of scientific data. How important are clear graphics to our understanding of these data? Defend your opinion.
Find the latest data for the atmospheric carbon dioxide concentration. Is the level still rising? How fast is it rising?
Discuss some of the factors that will affect the future concentration of carbon dioxide in the atmosphere. What do you think should be done to slow or stop the growth in the carbon dioxide
In the past, a carbon dioxide concentration of 300 parts per million accompanied global average temperatures as much as about 9°F (5°C) higher than the global average temperature today. What do you
Study Figure 46 carefully. How does the carbon dioxide concentration today compare to that of 1750? How does that of 1750 compare to that during the past 800,000 years? What conclusions can you draw
Discuss how you might make a similar graph for some other historical or political event.

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