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nonparametric statistical inference
Questions and Answers of
Nonparametric Statistical Inference
If r = 0.200, then r2 = 0.040 and 4% of the plotted points lie on the line of best fit.determine whether the given statement is true or false.
Refer again to the scatterplot in Figure 23.Does there appear to be a significant correlation between the two variables?
For a collection of paired sample data, the correlation coefficient is found to be -0.099. Which of the following statements best describes the relationship between the two variables?a. There is no
Which of the following are likely to have a correlation?a. SAT scores and weights of randomly selected subjectsb. Reaction times and IQ scores of randomly selected subjectsc. Height and arm span of
Fill in the blanks: Every possible correlation coefficient must lie between the values of _____ and _____.
Examine the scatterplot in Figure 22 and estimate the value of the correlation coefficient. 3 4 54 6 986 7 2 0 1 2 3 4 5 6789
A researcher collects paired sample data and computes the value of the linear correlation coefficient to be 0.Based on that value, he concludes that there is no relationship between the two
You are considering the most expensive purchase that you are likely to make: the purchase of a home. Identify at least five different variables that are likely to affect the actual value of a home.
In a study of randomly selected subjects, it is found that there is a strong correlation between household income and number of visits to dentists. Is it valid to conclude that higher incomes cause
For 10 pairs of sample data, the correlation coefficient is computed to be r = -1. What do you know about the scatterplot?
In a study of global warming, assume that we have found a strong positive correlation between carbon dioxide concentration and temperature. Identify three possible explanations for this correlation.
In a study of casino size (square feet) and revenue, the value of r = 0.445 is obtained. Find the value of r 2. What does that value tell us?
Can we conclude that the old ratings have a direct causal effect on the new ratings? Explain briefly.refer to the combined city–highway fuel economy ratings (mi/gal) for different cars. The old
Estimate the value of the correlation coefficient. What does that value suggest?refer to the combined city–highway fuel economy ratings (mi/gal) for different cars. The old ratings are based on
Construct a scatterplot. What does the result suggest?refer to the combined city–highway fuel economy ratings (mi/gal) for different cars. The old ratings are based on tests used before 2008 and
Legal Causation. Find a news report concerning an ongoing legal case, either civil or criminal, in which establishing causality is important to the outcome.Briefly describe the issue of causation in
Causation in the news. Find a recent news report in which a statistical study led to a conclusion of causation. Describe the study and the claimed causation. Do you think the claim of causation is
Dietary Fiber and Coronary heart Disease. In the largest study of how dietary fiber prevents coronary heart disease (CHD) in women (Journal of the American Medical Association, Vol. 281, No. 21),
air Bags and Children. Starting from the Web site of the National Highway Traffic Safety Administration, research the latest studies on the safety of air bags, especially with regard to children.
Vasectomies and Prostate Cancer. An article titled “Does Vasectomy Cause Prostate Cancer?” (Chance, Vol. 10, No. 1)reports on several large studies that found an increased risk of prostate cancer
gun Control. Those who favor gun control often point to a positive correlation between the availability of handguns and murder rates to support their position that gun control would save lives. Does
high-Voltage Power Lines. Suppose that people living near a high-voltage power line have a higher incidence of cancer than people living farther from the power line. Can you conclude that the
older moms. A study reported in Nature claims that women who give birth later in life tend to live longer. Of the 78 women who were at least 100 years old at the time of the study, 19%had given birth
Longevity of orchestra Conductors. A famous study in Forum on Medicine concluded that the mean lifetime of conductors of major orchestras was 73.4 years, about 5 years longer than that of all
other Lung Cancer Causes. Several things besides smoking have been shown to be probabilistic causal factors in lung cancer. For example, exposure to asbestos and exposure to radon gas, both of which
Smoking and Lung Cancer. There is a strong correlation between tobacco smoking and incidence of lung cancer, and most physicians believe that tobacco smoking causes lung cancer. Yet, not everyone who
Identifying Causes: headaches. You are trying to identify the cause of late-afternoon headaches that plague you several days each week.For each of the following tests and observations, explain which
IQ and Pulse rate. People with higher resting pulse rates (beats per minute) tend to have higher IQ scores.determine whether the stated causal connection is valid. If the causal connection appears to
Drinking and reaction Time. Drinking greater amounts of alcohol decreases a person’s reaction time.determine whether the stated causal connection is valid. If the causal connection appears to be
magnet Treatment. Heart disease can be cured by wearing a magnetic bracelet on your wrist.determine whether the stated causal connection is valid. If the causal connection appears to be valid,
Test grades. Test grades are affected by the amount of time and effort spent studying and preparing for the test.determine whether the stated causal connection is valid. If the causal connection
Smoking and Cotinine. When the body absorbs nicotine, it converts it into cotinine. Experiments have ruled out coincidence as an explanation for a correlation between exposure to second-hand smoke
Smoking and Cotinine. A study showed that there is a correlation between exposure to second-hand smoke and the measured amount of cotinine in the body. We can establish that exposure to second-hand
Value of r. A variable can have a direct causal effect on another variable only if the correlation coefficient is given by r = 1.decide whether the statement makes sense (or is clearly true) or does
Value of r. When analyzing paired sample data, the value of the correlation coefficient r allows us to determine whether one variable has a direct causal effect on the other.decide whether the
Correlation and Causality. What is the difference between finding a correlation between two variables and establishing causality between two variables?
Confounding Variable. What is a confounding variable?How can a confounding variable create a situation in which an underlying causality is hidden?
role of Experiments. In theory, we can use experiments to rule out two of the three different explanations for the presence of a correlation between two variables. Which of the three explanations do
Correlation. Identify three different explanations for the presence of a correlation between two variables.
your own multiple regression. Come up with an example from your own life or work in which a multiple regression analysis might reveal important trends. Without actually doing any analysis, describe
Best-Fit Line in the news. Although scatterplots are rare in the news, they are not unheard of. Find a scatterplot of any kind in a news article (recent or not).Draw a best-fit line by eye. Discuss
Predictions in the news. Find a recent news report in which a correlation is used to make a prediction.Evaluate the validity of the prediction, considering all of the cautions described in this
Worldwide Population Indicators. The following table gives five population indicators for eleven selected countries. Study these data and try to identify possible correlations. Doing additional
asbestos. Research asbestos, its sources, and its effects.Discuss the correlations that have helped researchers understand adverse health effects from asbestos exposure.Discuss efforts to prevent
Lead Poisoning. Research lead poisoning, its sources, and its effects. Discuss the correlations that have helped researchers understand lead poisoning. Discuss efforts to prevent it.
Use both scatterplots for actual and predicted temperature in Figure 6.determine how much of the variation in the variable can be accounted for by the best-fit line.c. Briefly discuss whether you
Use the scatterplot for number of farms and size of farms in Figure 5.determine how much of the variation in the variable can be accounted for by the best-fit line.c. Briefly discuss whether you
Use the scatterplot for life expectancy and infant mortality in Figure 4.determine how much of the variation in the variable can be accounted for by the best-fit line.c. Briefly discuss whether you
Use the scatterplot for color and price in Figure 2.determine how much of the variation in the variable can be accounted for by the best-fit line.c. Briefly discuss whether you could make valid
old Faithful. Using paired sample data consisting of the duration time (in seconds) of eruptions of Old Faithful geyser and the time interval (in minutes) after the eruption, a value of r2 = 0.926 is
height and Weight. Using data from the National Health Survey, the equation of the best-fit line for women’s heights and weights is obtained, and it shows that a woman 120 inches tall is predicted
r 2 Value. A value of r2 = -0.040 is obtained from a sample of men, with each pair of data consisting of the height in inches and the SAT score for one man.decide whether the statement makes sense
r 2 Value. A value of r2 = 1 is obtained from a sample of paired data with one variable representing the amount of gas (gallons) purchased and the total cost of the gas.decide whether the statement
regression. An investigator has data consisting of heights of daughters and the heights of the corresponding mothers and fathers. She wants to analyze the data to see the effect that the height of
r 2.For a study involving paired sample data, it is found that r = -0.4. What is the value of r 2? In general, what is r2 called, what does it measure, and how can it be interpreted? That is, what
Best-Fit Line. What is a best-fit line (also called a regression line)? How is a best-fit line useful?
Well-Interpreted Correlations. Find a recent news report in which you believe that a correlation has been presented with a reasonable interpretation. Describe the correlation and the reported
misinterpreted Correlations. Find a recent news report in which you believe that a correlation may have been misinterpreted. Describe the correlation, the reported interpretation, and the problems
real Correlations.a. Describe a real situation in which there is a positive correlation that is the result of coincidence.b. Describe a real situation in which there is a positive correlation that is
Football-Stock update. Find data for recent years concerning the Super Bowl winner and the end-of-year change in the stock market (positive or negative). Do recent results still agree with the
reading and Test Scores. The following (hypothetical)data set gives the number of hours 10 sixth-graders read per week and their performance on a standardized verbal test(maximum of 100).a. Construct
Birth and Death rates. Figure 17 shows the birth and death rates for different countries, measured in births and deaths per 1,000 population.a. Estimate the correlation coefficient and discuss
grouped Temperature Data. The following table shows the average January high temperature and the average July high temperature for 10 major cities around the world.a. Construct a scatterplot for the
grouped Shoe Data. The following table gives measurements of weight and shoe size for 10 people (including both men and women).a. Construct a scatterplot for the data. Estimate or compute the
outlier Effects. Consider the scatterplot in Figure 16.a. Which point is an outlier? Ignoring the outlier, estimate or compute the correlation coefficient for the remaining points.b. Now include the
outlier Effects. Consider the scatterplot in Figure 15.a. Which point is an outlier? Ignoring the outlier, estimate or compute the correlation coefficient for the remaining points.b. Now include the
melanoma and Latitude. Some studies have shown that, for certain ethnic groups, the incidence of melanoma (the most dangerous form of skin cancer) increases as latitude decreases.In each case, state
gas and Driving. It has been found that as gas prices increase, the distances vehicles are driven tend to get shorter.In each case, state the correlation clearly.(For example, we might state that
galaxies. Astronomers have discovered that, with the exception of a few nearby galaxies, all galaxies in the universe are moving away from us. Moreover, the farther the galaxy, the faster it is
Traffic Lights and Car Crashes. It has been found that as the number of traffic lights increases, the number of car crashes also increases.In each case, state the correlation clearly.(For example, we
Vehicles and Waiting Time. It has been found that as the number of registered vehicles increases, the time drivers spend sitting in traffic also increases.In each case, state the correlation
Study Time. Statistics students find that as they spend more time studying, their test scores are higher.In each case, state the correlation clearly.(For example, we might state that “there is a
running and Weight. It has been found that people who exercise regularly by running tend to weigh less than those who do not run, and those who run longer distances tend to weigh less than those who
guns and Crime rate. In one state, the number of unregistered handguns steadily increased over the past several years, and the crime rate increased as well.
Causation. If we have two variables with one being the direct cause of the other, then there may or may not be a correlation between those two variables.decide whether the statement makes sense (or
Causation. If we conduct a study showing that there is a strong negative correlation between resting pulse rate and amounts of time spent in rigorous exercise, we can conclude decreases in resting
Causation. If we have 20 pairs of sample data with a correlation coefficient of 1, then we know that one of the two variables is definitely the cause of the other.decide whether the statement makes
Scatterplot. A set of paired sample data results in a correlation coefficient of r = 0, so the scatterplot will show that there is no pattern of the plotted points.decide whether the statement makes
Scatterplot. Does a scatterplot reveal anything about a cause and effect relationship between two variables?
outliers. When studying salaries paid to CEOs of large companies, it is found that almost all of them range from a few hundred thousand dollars to several million dollars, but one CEO is paid a
SIDS. An article in the New York Times on infant deaths included a statement that, based on the study results, putting infants to sleep in the supine position decreased deaths due to SIDS (sudden
Correlation and Causality. In clinical trials of the drug Lisinopril, it is found that increased dosages of the drug correlated with lower blood pressure levels. Based on the correlation, can we
your own negative Correlations. Give examples of two variables that you expect to be negatively correlated. Explain why the variables are correlated and why the correlation is (or is not) important.
your own Positive Correlations. Give examples of two variables that you expect to be positively correlated. Explain why the variables are correlated and why the correlation is (or is not) important.
Correlations in the news. Find a recent news report that discusses some type of correlation. Describe the correlation. Does the article give any sense of the strength of the correlation? Does it
height and Pulse rate. Select a sample of at least eight people and record each person’s pulse rate by counting the number of heartbeats in 1 minute. Also record each person’s height. Using the
height and arm Span. Select a sample of at least eight people and measure each person’s height and arm span.(When you measure arm span, the person should stand with arms extended like the wings on
Statistical abstract. Explore the “frequently requested tables” at the Web site for the Statistical Abstract of the United States. Choose data that are of interest to you and explore at least two
Success in the nFL. Find last season’s NFL team statistics. Construct a table showing the following for each team:number of wins, average yards gained on offense per game, and average yards allowed
unemployment and Inflation. Use the Bureau of Labor Statistics Web page to find monthly unemployment rates and inflation rates over the past year. Construct a scatterplot for the data. Do you see any
Changing units of measurement. The correlation coefficient remains unchanged if we change the units used to measure x, y, or both.determine whether the given property is true, and explain your answer.
Interchanging Variables. The correlation coefficient remains unchanged if we interchange the variables x and y.determine whether the given property is true, and explain your answer.
Calories and Infant mortality. Consider the following table showing mean daily caloric intake (all residents) and infant mortality rate (per 1,000 births) for 10 countries.a. Construct a scatterplot
retail Sales. Consider the following table showing one year’s total sales (revenue) and profits for eight large retailers in the United States.a. Construct a scatterplot for the data.b. Briefly
January Weather. Consider the following table showing January mean monthly precipitation and mean daily high temperature for ten Northern Hemisphere cities (National Oceanic and Atmospheric
TV Time. Consider the following table showing the average hours of television watched in households in five categories of annual income.a. Construct a scatterplot for the data. To locate the dots,
movie Data. Consider the following table showing total box office receipts and total attendance for all American films.a. Construct a scatterplot of the data.b. Briefly characterize the correlation
Brain Size and Intelligence. The table below lists brain sizes (in cm3) and Wechsler IQ scores of subjects (based on data from “Brain Size, Head Size, and Intelligence Quotient in Monozygatic
Safe Speeds? Consider the following table showing speed limits and death rates from automobile accidents in selected countries.a. Construct a scatterplot of the data.b. Briefly characterize the
Two-Day Forecast. Figure 8 shows a scatterplot in which the actual high temperature for the day is compared with a forecast made two days in advance. Estimate the correlation coefficient and discuss
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