(This problem is based on an example from the column “Ask Marilyn” in Parade magazine.) A company runs two trials of two treatments for an illness. In the first trial, Treatment A cures 20% of the cases (40 out of 200) and Treatment B cures 15% of the cases (30 out of 200). In the second trial, Treatment A cures 85% of the cases (85 out of 100) and Treatment B cures 75% of the cases (300 out of 400). Which treatment had the better cure rate in the two trials individually? Which treatment had the better overall cure rate? Explain why the results might seem surprising or paradoxical, and how the paradox can be resolved.
> In a study of facial behavior, people in a control group are timed as to the duration of eye contact they make in a 5-minute period. Their times are normally distributed with a mean of 184.0 seconds and a standard deviation of 55.0 seconds (based on data
> Pulse rates for adult females are normally distributed with a mean of 74.0 beats per minute (bpm) and a standard deviation of 12.5 bpm. Use the 68-95-99.7 rule to find the following values. a. Percentage of pulse rates less than 74 bpm b. Percentage of p
> A test of depth perception is designed so that scores are normally distributed with a mean of 50 and a standard deviation of 10. Use the 68-95-99.7 rule to find the following values. a. Percentage of scores less than 50 b. Percentage of scores less than
> I found the standard score of the data value, even though I do not know the standard deviation of the data set.
> My good grades are a result of the fact that the number of hours I study each week put me in the 90th percentile for study time.
> My height puts me in the 37th percentile for my gender, which means my height has a negative standard score.
> Briefly describe the four conditions under which we can expect a data set to have a nearly normal distribution. Give an example of a set of data that might be approximated by the normal distribution.
> What does the area under the normal distribution curve represent? What is the total area under the normal distribution curve?
> Draw a rough sketch of a normal distribution. Do all normal distributions look the same?
> You want to determine the average (mean) number of robocalls received each day by adults in Alaska. • Sample 1: The 537 adults in Alaska who respond to a survey published in a newspaper • Sample 2: The first 537 people to visit a particular Anchorage
> The graph in Figure 3.21 shows home prices in different regions of the United States. a. Describe general trends that apply to the home price data for all regions. b. Describe any differences that you notice among the different regions. Figure 3.21
> When we refer to a “normal” distribution, does the word normal have the same meaning as it does in ordinary usage? Explain.
> Consider the graph of the normal distribution in Figure 5.15, which gives the relative frequencies in a distribution of body weights for a sample of male students. a. What is the mean of the distribution? b. Estimate (using area) the percentage of studen
> Consider the graph of the normal distribution in Figure 5.14, which illustrates the relative frequencies in a distribution of systolic blood pressures (in standard units of millimeters of mercury) for a sample of female students. The distribution has a s
> Consider the graph of the normal distribution in Figure 5.13, which shows the relative frequencies in a distribution of IQ scores. The distribution has a mean of 100 and a standard deviation of 16. a. What is the total area under the curve? b. Estimate (
> Consider the graph of the normal distribution in Figure 5.12, which gives relative frequencies in a distribution of men’s heights. The distribution has a mean of 69.6 inches and a standard deviation of 2.8 inches. a. What is the total a
> Figure 5.11 shows a histogram for the weights (in grams) of 100 randomly selected M&M plain candies. Is this distribution close to normal? Should this variable have a normal distribution? Why or why not? Figure 5.11
> Figure 5.10 on the next page shows a histogram for the departure delay times (in minutes) of 152 American Airlines flights from Los Angeles to San Francisco. Is this distribution close to normal? Should this variable have a normal distribution? Why or wh
> The amount of nicotine absorbed by the human body can be determined by measuring the amount of cotinine (ng/ml) in the blood. Figure 5.9 shows a histogram for the amounts of cotinine measured in 40 adults who do not smoke but are exposed to second-hand s
> Figure 5.8 shows a histogram for the body temperatures (in °F) of 500 randomly selected adults. Is this distribution close to normal? Should this variable have a normal distribution? Why or why not? Figure 5.8
> The amounts of income tax paid by 5000 randomly selected U.S. adults.
> The stack plot in Figure 3.20 shows the numbers of higher education students enrolled in public and private colleges. The last few bars are projections from the U.S. National Center for Education Statistics. a. Describe any trends revealed on this graphi
> In a Gallup poll of 1059 randomly selected adults, 39% answered “yes” when asked “Do you have a gun in your home?”
> The departure delay times (in minutes past the scheduled time) of Amtrak trains leaving New York City for Boston.
> The outcomes of many tosses of a single die with 12 sides numbered 1 through 12.
> The measured systolic blood pressure of randomly selected adult males.
> The measured voltage amounts from newly manufactured AAA batteries made by Duracell.
> The pulse rates of randomly selected adult females.
> The winning numbers drawn in California’s Daily Four lottery game, in which four digits between 0 and 9 are drawn and digits can be repeated.
> The amounts of rainfall (in inches) on each day of a year in Boston.
> Identify the distribution in Figure 5.7 that is not normal. Of the two normal distributions, which has the larger standard deviation? Figure 5.7
> Identify the distribution in Figure 5.6 that is not normal. Of the two normal distributions, which has the larger standard deviation? Figure 5.6
> Every 100th iPhone screen is tested for readability
> Refer to the QWERTY data in Exercise 21 in Section 3.1 and construct a dot plot.
> The distribution of annual incomes of U.S. adults is a normal distribution.
> A pollster conducts a research project about how adult Americans pay their bills. She posts her survey on a website and obtains 47 responses.
> The distribution of the weights of all adult elephants in Kenya is a normal distribution.
> The distribution of Chrome book sales data over the last year is not normal, because it has two modes corresponding to the holiday season and back-to-school season.
> Among a sample of 1037 adult women, pulse rates are normally distributed with a mean of 74.0 beats per minute, but 75% of the women have pulse rates greater than 74.0 beats per minute.
> 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 a defect rate of 4% at the other site. Therefore, the overall rate of defects must be 3%.
> Siena wins each of the first two sets of a tennis tournament by winning more games than her opponent in the first set and also winning more games than her opponent in the second set. It follows that Siena won more games than her opponent overall in the f
> When the Giants and Patriots football teams play each other, is it possible for one of the quarterbacks to have a higher passing percentage in each half while having a lower passing percentage for the entire game?
> If you are pulled over while driving and given a breathalyzer test for alcohol, what is the result called if the test incorrectly indicates that you have consumed alcohol?
> A professional soccer player is given a test for a banned substance. What does it mean when she is told that the result is positive? Do we know from such a positive result whether the player actually used the banned substance?
> When constructing a histogram of blood platelet counts, it is better to use three-dimensional bars in the graph.
> Professional athletes are routinely barred from participation for using banned substances. For such a test, what is a false positive? What is a false negative? What is a true positive? What is a true negative?
> The New York State Department of Health estimates a 10% rate of HIV infection among the at-risk population and a 0.3% rate in the general population. Tests for HIV are 95% accurate in detecting both true negatives and true positives. Random selection and
> The sexuality of women was discussed in Shere Hite’s book Women and Love: A Cultural Revolution in Progress. Her conclusions were based on sample data from 4500 mailed responses obtained from 100,000 questionnaires that were sent to women.
> The 95% confidence interval for a poll suggested that support for Governor Garcia is between 55% and 60%. Therefore, we can be certain that a majority of the population supports the governor.
> (This problem is based on an example in the column “Ask Marilyn” in Parade magazine.) A company decided to expand, so it opened a factory, generating 455 jobs. For the 70 white-collar positions, 200 males and 200 females applied. Of the females who appli
> 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 4000 patients, the incidence rate of the disease matches the national
> 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). In each case, it was known whether the subject lied, so the table in
> Two drugs, A and B, were tested on a total of 2000 patients, half of whom were women and half of whom were men. Drug A was given to 900 patients and Drug B to 1100 patients. The results appear in the following table. a. Give numerical evidence to suppor
> 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 than Morehouse College. b. Give numerical evidence to support the claim that
> A graphic artist for a magazine depicts the populations of the 10 largest U.S. cities by using bars of different heights, with the bars positioned on the locations of the cities on a map of the United States.
> Two cross-country running teams, called the Gazelles and the Cheetahs, participated in a (hypothetical) study in which 50% of the Gazelles and 65% of the Cheetahs used weight training to supplement a running workout. The remaining runners did not use wei
> 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 New York City. b. Compute the death rates for whites, nonwhites, and all re
> 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 general terms, how did the SAT scores of the students in the five
> 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 for all races. a. Which state had the higher scores in both racial c
> A KRC Research poll of 1002 randomly selected adults found that 53% of them said that they feel vulnerable to identity theft.
> 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 half? Who had the higher completion percentage in the second half? Who had the
> The table below shows the batting records of two baseball players in the first half (first 81 games) and second half of a season. Who had the higher batting average in the first half of the season? Who had the higher batting average in the second half? W
> When taking a test for pregnancy, a true negative result is the same as a true positive result.
> After being tested for the presence of a disease, a patient is told to think positively, so the patient is hoping for a positive test result.
> Briefly describe how you find quartiles and percentiles for a data set.
> I used a contour map to show the ages of full-time students at my college.
> Briefly distinguish between the following measures of variation: range, five-number summary, and standard deviation. Which one(s) can be represented with a boxplot?
> Consider two grocery stores at which the mean waiting time in line is the same but the variation of waiting times is different. At which store would you expect the customers to have more complaints about the waiting time? Explain.
> For the past 100 years, the mean batting average of major league baseball players has remained fairly constant at about 0.260. However, the standard deviation of batting averages has decreased from about 0.049 in the 1870s to 0.031 today. What does this
> 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 deviation of 0.55, while the annual percentage returns for portfolios with 32 stocks h
> You manage a small ice cream shop in which employees scoop the ice cream by hand. Each night, you total the day’s sales and the total volume of ice cream sold. You find that on nights when an employee named Ben is working, the mean price of the ice cream
> You want to determine the average (mean) annual salary of the current members of Congress.
> 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 produces batteries with a mean output of 12.1 volts and a standard deviat
> The following data sets give the approximate lengths (in minutes) of Beethoven’s nine symphonies and Mahler’s nine symphonies.
> 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 their inaugurations.
> The following data sets give the driving speeds (in mi/h) of the first nine cars to pass through a school zone and the first nine cars to pass through a downtown intersection.
> Reasoning that barrels of oil are three-dimensional, a newspaper publishes a three-dimensional graph showing oil production (barrels) in five different years.
> 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.
> The following four sets of seven 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, 6, 7} ……{3, 3, 3, 6, 9, 9, 9} a. Make a histogram for each set. b. Give the five-number summary and draw a boxplot for each se
> The following four sets of seven 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. Construct a histogram for each set. b. Give the five-number summary and draw a box
> A data set consists of the ages of 87 female actors at the time they won an Academy Award. a. One of the women was 50 years old, and she was older than 77 of the other winners. What is the percentile of the age of 50? b. One of the women was 25 years old
> 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 465 M&Ms weighed 0.776 gram and it was heavier than 25 of the other M&Ms. What is the percentile of this particular value? b. O
> Waiting times (in minutes) of customers at the Jefferson Valley Bank (where all customers enter a single waiting line) and the Bank of Providence (where customers wait in individual lines at three different teller windows) are listed below.
> You want to determine the mean age of all statistics students in the United States.
> Listed below are contributions (in dollars) made to the two presidential candidates in a recent election. All contributions are from the same ZIP code. (The data are from the Huffington Post.)
> Listed below are amounts (in millions of dollars) collected from parking meters by Brinks and others in New York City during similar time periods. A larger data set was used to convict five Brinks employees of grand larceny. (The data were provided by th
> Listed below are speeds (in mi/h) of cars on the New Jersey Turnpike. All cars are going in the same direction, and all of the cars are from New Jersey. The speeds were measured with a radar gun, and the researchers observed the races of the drivers. (Th
> What is info graphic, and what is its goal?
> Listed below are measurements of “specific absorption rate” (SAR) of radiation (in W/kg) when these types of cell phones are held to the head: Samsung SGHtss9, Blackberry Storm, Blackberry Curve, Motorola Moto, T-Mobile Sidekick, Sanyo Katana Eclipse, Pa
> Listed below are measurements of blood alcohol concentration (BAC) 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 0.24 0.14 0.16 0.12 0.16
> The following are the body temperatures (in °F) of randomly selected normal, healthy adults: 98.6 ……98.6 ……98.0 ……98.0 ……99.0 98.4 ……98.4 ……98.4 ……98.4 ……98.6
> The following times (in seconds) were recorded when statistics students participated in an experiment to test their ability to determine when 1 minute (60 seconds) had passed: 53…… 52 ……75 ……62 ……68 ……58 ……49 ……49
> Listed below are the numbers on the jerseys of the starting lineup for the New Orleans Saints when they won their first Super Bowl football game. Does it make sense to compute the range and standard deviation for these data? 9 ……23 ……25 ……88 ……12 ……19 ……
> Ayurveda is a traditional medical system commonly used in India. Listed below are the lead concentrations (in g/g) measured in different Ayurveda medicines (manufactured in the United States). (Data from “Lead, Mercury, and Arsenic in U.S. and Indian Ma
> Listed below are measurements of the “head injury criterion” (hic) for the following seven small cars tested in crashes by the National Highway Traffic Safety Administration: Chevrolet Aveo, Honda Civic, Volvo S40, VW Jetta, Hyundai Elantra, Kia Rio, and
> You want to determine the mean weight of all high school football players in the state of California.
> Listed below are the earnings (in millions of dollars) of the celebrities with the five highest incomes in a recent year. The celebrities in order are Steven Spielberg, Howard Stern, George Lucas, Oprah Winfrey, and Jerry Seinfeld. 332 ……302 ……235 ……225
> The scores on the statistics exam had the following results: range 40; high 98; low 58; median 81; standard deviation 8.
> What is a three-dimensional graphic? When is this type of graphic just cosmetic, and when is it helpful? What are its advantages and disadvantages?
> The standard deviation for the heights of 5-year-old children is smaller than the standard deviation for the heights of children who range in age from 3 to 15.
