Data showed a strong correlation between exposure to second-hand smoke and the measured amount of cotinine in the body. Follow-up experiments ruled out coincidence as an explanation for this correlation, and biologists identified a mechanism by which second-hand smoke exposure could lead to cotinine in the bloodstream. We can therefore be confident that exposure to second-hand smoke causes higher blood levels of cotinine.
> What is the t distribution? What factors determine its shape? Describe conditions under which you could use a t distribution instead of a normal distribution when making inferences about a population mean.
> Use the sample data listed in Exercise 18 with a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1.6 W/kg.
> Use the sample data listed in Exercise 17 with a 0.05 significance level to test the claim that the sample is from a population with a mean equal to 1000 cm3.
> The Carolina Tobacco Company advertised that its best-selling non filtered cigarettes contain 40 milligrams of nicotine or less, but Consumer Advocate magazine ran tests on 10 randomly selected cigarettes and found the amounts (in milligrams) shown below
> The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in the standard unit “head injury condition” (hic). The safety requirement fo
> One of the authors of this text claimed that his pulse rate was lower than the mean pulse rate of statistics students. The author’s pulse rate was measured and found to be 60 beats per minute, and the 20 students in his class measured their pulse rates.
> If one of the subjects is randomly selected, find the probability of selecting someone who lied or did not lie.
> When birth weights were recorded for a simple random sample of 16 male babies born to mothers taking a special vitamin supplement, the sample had a mean of 3.675 kilograms and a standard deviation of 0.657 kilogram (based on data from the New York State
> The mean time between failures for a Telektronic Company radio used in light aircraft is 420 hours. After 15 new radios were modified in an attempt to improve reliability, tests were conducted to measure the times between failures. The 15 radios had a me
> The U.S. Mint has a specification requiring that pennies have a mean weight of 2.5 grams (g). Thirty randomly selected pennies have a mean weight of 2.49910 g and a standard deviation of 0.01648 g. The mean weight of all pennies is assumed to be normally
> Students randomly selected 30 people and measured the accuracy of their wristwatches, with positive errors representing watches that were ahead of the correct time and negative errors representing watches that were behind the correct time. The 30 values
> A simple random sample of 16 different cereals is obtained, and the sugar content (in grams of sugar per gram of cereal) is measured for each cereal selected. Those amounts have a mean of 0.295 gram and a standard deviation of 0.168 gram. The amount of s
> Listed below are the measured “specific absorption rates” (SARs) of radiation (in watts per kilogram, or W/kg) from a sample of cell phones (when held to the head). The data are from the Environmental Working Group. The media often present reports about
> Listed below are brain volumes (in cubic centimeters, or cm3) of adult subjects used in a study. Use the sample data to construct a 95% confidence interval estimate of the mean of the normally distributed brain volumes of the entire adult population. Giv
> Listed below are lengths (in minutes) of randomly selected movies. The lengths of all movies are assumed to be normally distributed. 110 96 125 94 132 120 136 154 149 94 119 132 a. Construct a 95% confidence interval estimate of the mean length of all mo
> Each car in a sample of seven cars was tested for nitrogen-oxide emissions (in grams per mile), and the following results were obtained: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15 (based on data from the Environmental Protection Agency). Assume that nitrog
> One of the authors of this text compiled a list of actual high temperatures and a corresponding list of three-day-forecast high temperatures. The difference for each day was then found by subtracting the three-day-forecast high temperature from the actua
> A two-way table, constructed from survey results, consists of two rows representing gender (male/female) and two columns representing the response to a question (yes/no). What is the null hypothesis for a test to determine whether there is some relations
> Estimate the probability that a randomly selected prime-time television show will be interrupted with a news bulletin.
> A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution that appears to be approximately bell-shaped with a mean of $9004 and a standard deviation of $5629 (based on da
> A simple random sample of epicenter depths of 51 earthquakes has a mean of 9.808 kilometers (km) and a standard deviation of 5.013 km. Determine the critical value of t and the margin of error, and then construct the 95% confidence interval estimate of t
> A simple random sample of men is obtained, and the elbow-to-fingertip length of each man is measured. The population of those lengths has a distribution that is normal. The sample statistics are n = 35, /= 14.5 inches, and s = 0.7 inch. Determine the cri
> A simple random sample of heights of basketball players in the NBA is obtained, and the population has a distribution that is approximately normal. The sample statistics are n = 16, /= 77.9 inches, and s = 3.50 inches. Determine the critical value of t a
> A simple random sample of IQ scores is selected from a normally distributed population of statistics professors. The sample statistics are n = 16, /= 130, and s = 10. Determine the critical value of t and the margin of error, and then construct the 95% c
> I was able to estimate the mean white blood cell count for the population of about 325 million people in the United States using a randomly selected sample of only 25 people.
> You want to test the claim that the mean annual income of all movie stars is greater than $1 million, but you know that income data are not normally distributed (they are right-skewed). Therefore you cannot use the t distribution to test the claim with a
> In testing a claim about a population mean, the t distribution is always used when the population standard deviation / is not known.
> You should always use the t distribution when the sample size is only n = 5.
> If a collection of paired sample data values yields a correlation coefficient of r = 1, then we can be very confident that causality is involved.
> If the hypothesis test of the claim described in Exercise 7 results in a P-value of 0.757, what do you conclude about the null hypothesis?
> Researchers conducted animal experiments to study smoking and lung cancer because it would have been unethical to conduct these experiments on humans.
> Describe three levels of confidence in causality that are used in the legal system, and briefly explain how these can be useful when we consider establishing causality with statistics.
> Briefly state in your own words the six guidelines that can be used in establishing causality.
> Briefly describe the correlations that made researchers suspect a link between smoking and lung cancer, and how causality was ultimately established.
> What is the difference between finding a correlation between two variables and establishing causality between two variables?
> The article “Does Vasectomy Cause Prostate Cancer?” (Chance, Vol. 10, No. 1) reports on several large studies that found an increased risk of prostate cancer among men with vasectomies. In the absence of a direct cause, several researchers attribute the
> Those who favor gun control often point to a positive correlation between the availability of handguns and the homicide rate to support their position that gun control would save lives. Does this correlation, by itself, indicate that handgun availability
> 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 high-voltage power line is the cause of the elevated cancer rate? If not, what other exp
> A study reported in Nature claims that women who give birth later in life tend to live longer. Of the 78women who were at least 100 years old at the time of the study, 19% had given birth after their 40th birthday. Of the 54women who were 73 years old
> 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 the mean lifetime of all American males at the time. The author claimed that a life of music causes a longer
> Assume that you want to test the claim that adult males in California, New York, Colorado, and Texas have the same mean height. What method would you use to test that claim?
> 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 are found in many homes, can cause lung cancer. Suppose that you meet a person wh
> 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 smokes gets lung cancer. Briefly describe how smoking could cause cancer when n
> When some people climb to higher altitudes without supplemental oxygen, they tend to experience increased physiological problems, such as headaches or disorientation. Briefly describe how the higher altitude could cause such problems when not all climber
> People who meditate more are likely to have higher incomes.
> Drinking greater amounts of alcohol decreases a person’s reaction time.
> Lower back pain can be reduced by exposing the back to a magnet.
> The time it takes to run a marathon is affected by the amount of time spent training for it.
> If causality has been established beyond reasonable doubt, then we can be 100% confident that the causality is real.
> What is multiple regression? When is it useful?
> What type of hypothesis test would be used to test the claim in Exercise 5: left-tailed, right-tailed, or two-tailed?
> What does the square of the correlation coefficient, r2, tell us about a best-fit line?
> Briefly list five important cautions to keep in mind when making predictions with bestfit lines.
> What is a best-fit line? How is a best-fit line useful?
> a. How well does the best-fit line actually fit the points in the scatterplot? b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r 2, identify how much of the variation in the variable can be accoun
> a. How well does the best-fit line actually fit the points in the scatterplot? b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r 2, identify how much of the variation in the variable can be accoun
> In each case, answer the following. a. How well does the best-fit line actually fit the points in the scatterplot? b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r 2, identify how much of the var
> In each case, answer the following. a. How well does the best-fit line actually fit the points in the scatterplot? b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r 2, identify how much of the var
> In each case, answer the following. a. How well does the best-fit line actually fit the points in the scatterplot? b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r 2, identify how much of the var
> In each case, answer the following. a. How well does the best-fit line actually fit the points in the scatterplot? b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r 2, identify how much of the var
> In each case, answer the following. a. How well does the best-fit line actually fit the points in the scatterplot? b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r 2, identify how much of the var
> What are the null and alternative hypotheses for a claim that the mean weight of NFL professional football players is greater than 200 pounds?
> In each case, answer the following. a. How well does the best-fit line actually fit the points in the scatterplot? b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r 2, identify how much of the var
> In seeking to understand the factors that affect a college graduate’s future income, researchers conducted a multiple regression analysis that examined the effects of major, grade point average, the ranking of the college, parental affluence, and parenta
> Using sample data on footprint lengths and heights from men, the equation of the best-fit line is obtained, and it is used to find that a man with a footprint length of 36 inches is predicted to have a height of 144 inches, or 12 feet.
> The data barely deviate at all from the best-fit line, and they produce this value for the square of the correlation coefficient: r2 = 0.3.
> I used a best-fit line for data showing the ages and heights of thousands of boys of various ages to predict the mean height of 9-year-old boys.
> If a correlation is very strong, can we conclude that one variable causes a change in the other variable? Why or why not?
> What are the three possible explanations for a correlation?
> Briefly explain how data that actually come from two distinct groups, both with strong correlations, can appear uncorrelated when grouped together. Does this mean that you should always break data into as many subgroups as possible? Why or why not?
> Briefly explain how an outlier can make it appear that there is correlation when there is none. Also briefly explain how an outlier can make it appear that there is no correlation when there is one. Under what circumstances is it reasonable to ignore out
> The scatterplot in Figure 7.18 depicts paired data values consisting of the weight (in grams) and year of manufacture for each of 72 pennies. a. Considering the complete collection of data, does there appear to be a correlation? b. Consider the grouping
> A simple random sample of 25 blood platelet counts is obtained from a normally distributed population with an unknown standard deviation. Which of the following distributions is most appropriate for a hypothesis test involving a claim about a population
> Figure 7.17 shows the birth and death rates for different countries, measured in births and deaths per 1000 people. Estimate the correlation coefficient, and discuss whether there is a strong correlation between the two variables. Notice that there appea
> The following table shows the average January high temperature and the average July high temperature (in °F) for 10 major cities around the world. Construct a scatterplot for the data. Estimate or compute the correlation coefficient. Based on
> The following table lists footprint length (in centimeters) and height (in centimeters) of 10 subjects (including both men and women). Use either a scatterplot or a formula for the linear correlation coefficient to determine whether there is a correlatio
> Consider the scatterplot in Figure 7.16. Which point is an outlier? Ignoring the outlier, estimate or compute the correlation coefficient for the remaining points. Now include the outlier. How does the outlier affect the correlation coefficient? Estimate
> Consider the scatterplot in Figure 7.15. Which point is an outlier? Ignoring the outlier, estimate or compute the correlation coefficient for the remaining points. Now include the outlier. How does the outlier affect the correlation coefficient? Estimate
> Data from the Centers for Disease Control and the Department of Energy show that as the numbers of people who drown in swimming pools increases, the power generated by nuclear plants also increases.
> It has been found that when gas prices increase, the distances that vehicles are driven tend to get shorter.
> Astronomers have discovered that, with the exception of a few nearby galaxies, all galaxies in the universe are moving away from our solar system. Moreover, the farther away the galaxy is, the faster it is moving away.
> It has been found that as the number of traffic lights increases, the number of car crashes also increases.
> Data from the National Vital Statistics Reports and the U.S. Department of Agriculture show that over the past several years in Maine, the divorce rate declined and per capita margarine consumption also declined.
> For the hypothesis test described in Exercise 1, which of the following distributions is most appropriate? a. normal distribution b. t distribution c. chi-square distribution d. uniform distribution
> Statistics students find that as they spend more time studying, their test scores are higher
> One study showed that there is a correlation between per capita cheese consumption and number of people who die by becoming tangled in their bedsheets. One variable increased while the other decreased over time.
> In one state, the number of unregistered handguns steadily increased over the past several years, and the crime rate increased as well.
> The correlation I found was so strong that a careful calculation showed it had less than a 1 in 100,000 probability of occurring by chance. Therefore, I can reasonably conclude that one variable is the cause of the other.
> A study showed that for one town, as the stork population increased, the number of human births in the town also increased. It therefore follows that the increase in the stork population caused the number of births to increase.
> If a scatterplot shows no correlation, then there cannot be any relationship between the two variables.
> I created a scatterplot of CEO salaries and corporate revenue for 10 companies and found a negative correlation, but when I left out a data point for a company whose CEO took no salary, there was no correlation for the remaining data.
> Define and distinguish between positive correlation, negative correlation, and no correlation. Give an example of each type of correlation
> What is a scatterplot, and how is one constructed? How can we use a scatter plot to investigate a correlation?
> What is a correlation? Give three examples of pairs of variables that are correlated.
> As part of the results from the test described in Exercise 1, the P-value of 0.001 is obtained. What do you conclude?
> Listed below are the ages of female and male Academy Award winners in 15 selected years. Each pair of ages is for the same year. Construct a scatterplot; Briefly characterize the correlation in words (such as “strong positive correlati
> A nonprofit organization held a fund-raising auction attended by one of the authors of this text. He recorded the opening bids suggested by the auctioneer and the final winning bids for several items. The amounts (in dollars) are listed below. Construct
> Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman (based on data from “Consistency of Blood Pressure Differences Between the Left and Right Arms,” by Eguchi, et al., Archives
> 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 Monozygotic Twins,” by Tramo etˆal., Neurology, Vol. 50
> Listed below are repair costs (in dollars) for cars crashed at 6 mi/h in full-front crash tests and the same cars crashed at 6 mi/h in full-rear crash tests (based on data from the Insurance Institute for Highway Safety). The cars are the Toyota Camry, M
