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nonparametric statistical inference

Questions and Answers of Nonparametric Statistical Inference

Distributions. For rolling a die, the mean outcome is 3.5.Can we apply the 68-95-99.7 rule and conclude that 95% of all outcomes fall within 2 standard deviations of 3.5? Why or why not?
standard score. The standard score for the height of a male is z = -2. Is the height of this male above or below the mean height of all males? How many standard deviations away from the mean is this?
standard score. Men’s heights are normally distributed with a mean of 69.0 in. and a standard deviation of 2.8 in. What is the standard z-score for a man with a height of 69.0 in.?
Non-normal Distributions. Find two variables in news reports that you suspect do not have nearly normal distributions. Explain your reasoning
Normal Distributions. Rarely does a news article refer to the actual distribution of a variable or state that a variable is normally distributed. Nevertheless, variables mentioned in news reports
movie Lengths. Collect data to support or refute the claim that movies have gotten shorter over the decades.Specifically, make a histogram of movie lengths for each decade from the 1940s through the
Finding Normal Distributions. Using the guidelines given in the text, choose a variable that you think should be nearly normally distributed. Collect at least 30 data values for the variable and make
saT score Distributions. The College Board Web site gives the distribution of SAT scores (usually in 50-point bins). Collect these data and construct a histogram for each part of the test. Discuss
Estimating areas. Consider the graph of the normal distribution in Figure 15, which gives the relative frequencies in a distribution of body weights for a sample of male students.a. What is the mean
Estimating areas. Consider the graph of the normal distribution in Figure 14, which illustrates the relative frequencies in a distribution of systolic blood pressures for a sample of female students.
areas and relative Frequencies. Consider the graph of the normal distribution in Figure 13, which shows the relative frequencies in a distribution of IQ scores. The distribution has a mean of 100 and
areas and relative Frequencies. Consider the graph of the normal distribution in Figure 12, which gives relative frequencies in a distribution of men’s heights. The distribution has a mean of 69.6
aspirin Weights. Figure 11 shows a histogram for the weights of 30 randomly selected aspirin tablets. The mean weight is 665.4 milligrams. Is this distribution close to normal? Should this variable
Quarter Weights. Figure 10 shows a histogram for the weights of 50 randomly selected quarters. The mean weight is 5.62 grams. Is this distribution close to normal? Should this variable have a normal
Pulse rates. Figure 9 shows a histogram for the pulse rates of 98 students. The mean pulse rate is 71.2 beats per minute. Is this distribution close to normal? Should this variable have a normal
movie Lengths. Figure 8 shows a histogram for the lengths of 60 movies. The mean movie length is 110.5 minutes. Is this distribution close to normal? Should this variable have a normal distribution?
Parking Ticket Fines. The amounts of the fines from parking tickets found on a random sample of 1,000 parked cars.state whether you would expect it to be normally distributed. Explain your reasoning.
Waiting Times. The waiting times at a bus stop if the bus comes once every 10 minutes and you arrive at random times.state whether you would expect it to be normally distributed. Explain your
Flight Delays. The lengths of time that commercial aircraft are delayed before departing.state whether you would expect it to be normally distributed. Explain your reasoning.
White Blood Cell Counts. The measured white blood cell counts of 500 randomly selected adult women.state whether you would expect it to be normally distributed. Explain your reasoning.
saT scores. All of the SAT scores from last year.state whether you would expect it to be normally distributed. Explain your reasoning.
Lottery. The numbers selected in the Pennsylvania “Match 6” lottery, in which players attempt to match six randomly selected numbers between 1 and 49.state whether you would expect it to be
Incomes. The incomes of randomly selected adults in the United States.state whether you would expect it to be normally distributed. Explain your reasoning.
Weights of Quarters. The exact weights of a random sample of quarters manufactured in 2012 by the U.S. Mint.state whether you would expect it to be normally distributed. Explain your reasoning.
What Is Normal? Identify the distribution in Figure 7 that is not normal. Of the two normal distributions, which has the larger standard deviation? 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 () (b)
What Is Normal? Identify the distribution in Figure 6 that is not normal. Of the two normal distributions, which has the larger standard deviation? 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 () (b)
salaries. An economist plans to obtain the current salaries of all professional football players, and she predicts that those salaries will have a normal distribution.decide whether the statement
IQ scores. The mean of a normally distributed set of IQ scores is 100, and 60% of the scores are over 105.decide whether the statement makes sense (or is clearly true) or does not make sense (or is
Brains. As part of a study of the relationship between brain size and IQ, a random sample of 250 adult males is obtained and their brain volumes are measured and found to be normally
heights of Women. A sample of 2,000 women is randomly selected, and it is found that the heights of the women are normally distributed with a mean of 63.6 in.decide whether the statement makes sense
areas. Birth weights in the United States are normally distributed with a mean (in grams) of 3420 g and a standard deviation of 495 g. If you graph this normal distribution, the area to the right of
random Digits. Many states have lotteries that involve the random selection of digits 0, 1, 2, …, 9.Is the distribution of those digits a normal distribution? Why or why not?
Normal Distribution. A normal distribution is informally and loosely described as a probability distribution that is“bell-shaped” when graphed. Draw a rough sketch of the bell shape that
Although economic data suggest that the vast majority of Americans are better off today than they were a few decades ago, the poorest Americans still live in difficult economic conditions. What do
Overall, do you think the increase in income inequality has been a good or bad thing for the United States? Will it be good if the trend continues? Defend your opinion.
Do you agree that the Pareto criterion is a good way to evaluate the ethics of economic change? Why or why not?
For example, does one seem to indicate a larger change in income inequality than the other? Can you think of other possible ways to display income data that might give a different picture than those
Compare several different ways of looking at the data shown in Figure 18 and Figure
Create your own “portfolio” of 10 stocks that you’d like to own, and assume you own 100 shares of each.Calculate the total value of your portfolio today, and track price changes over the next
The 30 stocks in the DJIA represent a sample of the more than 10,000 actively traded stocks, but it is not a random sample because it is chosen by particular editors for particular reasons that may
The DJIA is only one of many different stock market indices in wide use today. Briefly look up a few other indices, such as the S&P 500, the Russell 2000, and the NASDAQ. How do these indices differ
The stock market is still considered a riskier investment than, say, bank savings accounts or bonds. Nevertheless, financial advisors almost universally recommend holding at least some stocks, which
Identify the components that constitute the five-number summary for a data set.
Find the standard deviation of these body temperatures (°F):98.2, 98.2, 98.2, 98.2, and 98.2.
Use the range rule of thumb to estimate the standard deviation of the pulse rates given in Exercise 1.How does the result compare to the actual standard deviation of 10.9?
A standard test for braking reaction time of drivers is designed so that the mean is 2.00 sec and the standard deviation is 0.25 sec. Based on the range rule of thumb, what are the likely low and
Indicate whether the given statement could apply to a data set consisting of 1,000 values that are all different.a. The 20th percentile is greater than the 30th percentile.b. The median is greater
A histogram is constructed for a large set of pulse rates of adult males, and it is found that the distribution is symmetric and unimodal. What does this imply about the values of the mean and median?
The standard deviation of the pulse rates given in Exercise 1 is 10.9. What characteristic does that value measure?
What is the range of the pulse rates given in Exercise 1?
Find the median of the pulse rates given in Exercise 1.
When you add the pulse rates of 65, 74, 88, 77, and 92, then divide by the number of values, the result is 79.2.Which term best describes this value: average, mean, median, mode, or standard
a. What is the standard deviation for a sample of 50 values, all of which are the same?b. Which of the following two car batteries would you prefer to buy, and why?• One taken from a population
Combine the two samples from Review Exercise 1 and find the following:a. The percentile for the amount of 1.4 mgb. The mode
Nicotine in cigarettes. Listed below are the nicotine amounts (in mg per cigarette) for samples of filtered and non-filtered cigarettes. Do filters appear to be effective in reducing the amount of
Drug Testing and Athletes. Find a news report concerning drug testing of athletes. Summarize how the testing is being used, and discuss whether the testing is reliable.
Polygraphs. Find a recent article in which someone or some group proposes a polygraph test to determine whether a person is being truthful. In light of what you know about polygraph tests, do you
cancer Screening. Investigate recommendations concerning routine screening for some type of cancer (for example, breast cancer, prostate cancer, or colon cancer). Explain how the accuracy of the
Drug Testing. Explore the issue of drug testing either in the workplace or in athletic competitions. Discuss the legality of drug testing in these settings and the accuracy of the tests that are
Polygraph Arguments. Visit Web sites devoted to either opposing or supporting the use of polygraph tests.Summarize the arguments on both sides, specifically noting the role that false negative rates
hIV risks. The New York State Department of Health estimates a 10% rate of HIV for the at-risk population and a 0.3% rate for the general population. Tests for HIV are 95% accurate in detecting both
Drug Trials. (This problem is based on an example from the“Ask Marilyn” column in Parade Magazine.) A company runs two trials of two treatments for an illness. In the first trial, Treatment A
hiring Statistics. (This problem is based on an example in“Ask Marilyn” column in Parade Magazine.) A company decided to expand, so it opened a factory, generating 455 jobs. For the 70
Disease Test. Suppose a test for a disease is 80% accurate for those who have the disease (true positives) and 80%accurate for those who do not have the disease (true negatives). Within a sample of
Polygraph Test. The results in the table below are from experiments conducted by researchers Charles R.Honts (Boise State University) and Gordon H. Barland(Department of Defense Polygraph Institute).
better Drug. Two drugs, A and B, were tested on a total of 2,000 patients, half of whom were women and half of whom were men. Drug A was given to 900 patients and Drug B to 1,100 patients. The
basketball records. Consider the following (hypothetical)basketball records for Spelman and Morehouse Colleges.a. Give numerical evidence to support the claim that Spelman College has a better team
Weight Training. Two cross-country running teams participated in a (hypothetical) study in which a fraction of each team used weight training to supplement a running workout. The remaining runners
Tuberculosis Deaths. The following table shows deaths due to tuberculosis (TB) in New York City and Richmond, Virginia, in 1910.a. Compute the death rates for whites, nonwhites, and all residents in
Test Scores. Consider the following table comparing the grade point averages (GPAs) and mathematics SAT scores of high school students in 1988 and 1998 (before the SAT test format was revised).a. In
Test Scores. The table below shows eighth-grade mathematics test scores in Nebraska and New Jersey. The scores are separated according to the race of the student. Also shown are the state averages
Passing Percentages. The table below shows the passing records of two rival quarterbacks in the first half and second half of a football game.Who had the higher completion percentage in the first
batting Percentages. The table below shows the batting records of two baseball players in the first half (first 81 games) and last half of a season.Who had the higher batting average in the first
Test Accuracy. If a drug test is 90% accurate, it follows that 90% of those who test positive are actual drug users.decide whether the statement makes sense (or is clearly true) or does not make
Test results. After taking a test for the presence of a disease, a patient is happy because the physician announces that the test results are positive.decide whether the statement makes sense (or is
batting Average. Ann’s batting average for the first half of the softball season is higher than Bret’s, and Ann’s batting average for the second half of the season is higher than Bret’s. It
course Average. Ann and Bret are taking the same statistics course, in which the final grade is determined by assignments and exams. Ann’s mean score on the assignments is higher than Bret’s, and
better in Each half, Worse overall. When the Giants and Patriots football teams play each other, can one of the quarterbacks have a higher passing percentage in each half while having a lower passing
Test result. If you apply a test for the presence of alcohol, what is the result called if the test correctly indicates that the subject has not consumed alcohol?
Positive Test result. Jennifer is given a pregnancy test.What does it mean when she is told that the result is positive?
False Positive and False Negative. A baseball player is given a test for banned substances. For this test, what is a false positive? What is a false negative? What is a true positive? What is a true
Summarizing a News Data Set. Find an example of a data distribution given in the form of a table in a recent news report. Make a five-number summary and a boxplot for the distribution.
ranges in the News. Find two examples of data distributions in recent news reports; they may be given either as tables or as graphs. In each case, state the range of the distribution and explain its
Measuring Variation. The range and standard deviation use different approaches to measure variation in a data set.Construct two different data sets configured so that the range of the first set is
Kids and the Media. A recent study by the Kaiser Family Foundation looked at the role of media (for example, television, books, computers) in the lives of children. The report, which is on the Kaiser
Secondhand Smoke. At the Web sites of the American Lung Association and the U.S. Environmental Protection Agency, find statistical data concerning the health effects of secondhand (passive) smoke.
batting Standard Deviation. For the past 100 years, the mean batting average in the major leagues has remained fairly constant at about 0.260. However, the standard deviation of batting averages has
Portfolio Standard Deviation. The book Investments, by Zvi Bodie, Alex Kane, and Alan Marcus, claims that the annual percentage returns for investment portfolios with a single stock have a standard
Managing complaints. You manage a small ice cream shop in which your employees scoop the ice cream by hand. Each night, you total your sales and the total volume of ice cream sold. You find that on
Manufacturing. You are in charge of a manufacturing process that produces car batteries that are supposed to provide 12 volts of power. Manufacturing occurs at two different sites. The first site
The following data sets give the approximate lengths of Beethoven’s nine symphonies and Mahler’s nine symphonies (in minutes).Beethoven:28 36 50 33 30 40 38 26 68 Mahler:52 85 94 50 72 72 80 90
The following data sets show the ages of the first seven U.S. Presidents (Washington through Jackson) and seven recent U.S. Presidents (Ford through Obama) at the time of inauguration.First 7:57 61
The following data sets give the driving speeds in miles per hour of the first nine cars to pass through a school zone and the first nine cars to pass through a downtown intersection.School:20 18 23
The following data sets give the ages in years of a sample of cars in a faculty parking lot and a student parking lot at the College of Portland.Faculty:2 3 1 0 1 2 4 3 3 2 1 Student:5 6 8 2 7 10 1 4
understanding Standard Deviation. The following four sets of 7 numbers all have a mean of 6.{6, 6, 6, 6, 6, 6, 6}, {5, 5, 6, 6, 6, 7, 7}{5, 5, 5, 6, 7, 7, 7}, {3, 3, 3, 6, 9, 9, 9}a. Make a histogram
understanding Standard Deviation. The following four sets of 7 numbers all have a mean of 9.{9, 9, 9, 9, 9, 9, 9,} {8, 8, 9, 9, 9, 10, 10}{8, 8, 8, 9, 10, 10, 10} {6, 6, 6, 9, 12, 12, 12}a. Make a
calculating Percentiles. A data set consists of the 85 ages of women at the time that they won an Oscar in the category of best actress.a. One of the actresses was 40 years of age, and she was older
calculating Percentiles. A statistics professor with too much time on his hands weighed each M&M candy in a bag of 465 plain M&M candies.a. One of the M&Ms weighed 0.776 gram and it was heavier than
Treatment Effect. Researchers at Pennsylvania State University conducted experiments with poplar trees. Listed below are weights (in kilograms) of poplar trees given no treatment and poplar trees
Weather Forecast Accuracy. In an analysis of the accuracy of weather forecasts, the actual high temperatures are compared with the high temperatures predicted one day earlier and the high

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