Question: The price of a gallon of gas

> If you spent $23,875 for goods, services, and housing in 2014, what would the same purchases have cost in 1980?

> FICO (Fair Isaac Corporation) scores are routinely used to rate the quality of consumer credit. You want to determine the average (mean) FICO score of all adults in the United States.

> If you spent $12,250 for goods, services, and housing in 2000, what would the same purchases have cost in 2015?

> If you spent $12,250 for goods, services, and housing in 2015, what would the same purchases have cost in 2000?

> Adjusted for inflation, today’s price of $100 for that item is lower than the 1980 price of $50.

> My salary has remained the same for the past 10³years, but my standard of living has fallen.

> The CPI doubled from 1983 to 2006, so the price of gasoline also doubled over that time period.

> I’ve concluded that the CPI for 2016 is obsolete because it uses the prices of goods, services, and housing costs from 1982 to 1984 as its reference value.

> Explain the difference between the terms percent (%) and percentage points. Give an example of how they can differ for the same situation.

> Explain the difference between the key words of and more than when dealing with percentages. How are their meanings related?

> Distinguish between absolute and relative difference. Give an example that illustrates how we calculate a relative difference.

> Distinguish between absolute and relative change. Give an example that illustrates how we calculate a relative change.

> You want to determine the percentage of drivers who text while they are driving.

> In a Gallup poll of 1236 adult respondents, 5% said that bad luck follows breaking a mirror. That percentage has a margin of error of 1.2 percentage points. Why is it misleading to state that the percentage is 5% with a margin of error of 1.2%?

> A recent Super Bowl football game had a “77 share,” meaning that among the television sets in use at the time of the game, 77% were tuned to the game. a. If the percentage of 77% is in error by up to 4 percentage points, what are the possible values of t

> Based on current data, 99.3% of newborns survive the first five years of their lives, and 72.6% of people who reach age 80 years survive the next five years of their lives.

> The five-year survival rate for Caucasians for all forms of cancer increased from 39% in the 1960s to 61% now.

> The percentage of the world’s population living in developed countries decreased from 27.1% in 1970 to 16.4% now.

> In a test comparing vinyl and latex laboratory gloves, it was found that 63% of the vinyl gloves leaked (allowing viruses to pass through), but only 7% of the latex gloves leaked.

> A Pew Research Center survey of 3002 adults showed that the percentage who listen to National Public Radio is probably between 14% and 18% How should a newspaper report the margin of error? Explain.

> A Gallup poll of 1012 American adults showed that 89% of Americans say that human cloning should not be allowed. The margin of error was 3 percentage points. Would it matter if a newspaper reported the margin of error as “3%”? Explain.

> The Vice President’s salary is currently 42% less than the President’s salary, so the Vice President’s salary is ____% of the President’s salary.

> If the population of Montana is 20% less than the population of New Hampshire, then Montana’s population is ____% of New Hampshire’s population.

> A Harris Interactive survey of 514 human resources professionals showed that 46% of them say that piercings or tattoos are big grooming red flags. The margin of error for the survey was 4 percentage points.

> If the area of Norway is 24% more than the area of Colorado, then Norway’s area is ____ % of Colorado’s area.

> If a typical adult male is 8% taller than a typical adult female, then the typical adult male’s height is ____% of the typical adult female’s height.

> In a KRC Research poll of 1002 subjects, 53% said that they felt vulnerable to identity theft.

> In a Taylor Nelson Sofres Research survey of 703 workers, 61% of them said that they got their jobs through networking.

> In an Accountemps survey of 150 executives, 47% said that the most common job interview mistake is to have little or no knowledge of the company at which the interview is held.

> In a Harris poll of 514 human resource professionals, 46% said that body piercings and tattoos were big grooming red flags.

> Last year, France had 82 million international tourists. The United States had 63 million international tourists.

> Chicago’s O’Hare Airport handled 67 million passengers last year. The busiest airport in the world, Atlanta’s Hartsfield Airport, handled 95 million passengers last year.

> Last month, 34,781 Toyota Camry cars were sold, and there were 10,096 Ford Mustangs sold.

> The daily circulation of the Wall Street Journal is currently 2.38 million (the largest in the country). The daily circulation of the New York Times is currently 1.87 million (the second largest in the country).

> In a Gallup poll of 557 randomly selected adults, 51% said that they were underpaid. The margin of error is 4 percentage points.

> There were 1,038,280 bankruptcy cases filed last year, and in the year 2000 there were 1,276,900 bankruptcy cases filed.

> The U.S. population is now 323,447,281, and in 2000 it was 282,171,957.

> There are now 256 million registered passenger cars, and in 1990 there were 193 million.

> The number of daily newspapers in the United States is now 1486, and it was 2226 in 1990.

> A New York Times editorial criticized a chart caption that described a dental rinse as one that “reduces plaque on teeth by over 300%.” If the dental rinse removes all of the plaque, what percentage is removed? Is it possible to reduce plaque by over 300

> Media commonly report survey results giving the sample size and some percentage, but technology typically requires the actual number of particular responses instead of the percentage. In a Harris survey of 514 human resource professionals, 90% said that

> A study was conducted to determine whether flipping a penny or spinning a penny has an effect on the proportion of heads. Among 49,437 trials, 29,015 involved flipping pennies, and 14,709 of those pennies turned up heads. The other 20,422 trials involved

> A study was conducted of pleas made by 1348 criminals. Among those criminals, 956 pleaded guilty and 392 of them were sentenced to prison. Among 72 other criminals who pleaded not guilty, 58 were sent to prison (based on data from “Does It Pay to Plead G

> Express the following numbers in the three forms of fraction, decimal, and percentage. a. 275% b. 3.75 c. -0.45 d. 90%

> Express each of the following numbers in the three forms of fraction, decimal, and percentage. a. 3/5 b. 0.8 c. 150% d. -25%

> A study of 3005 adults aged 57 to 85 showed that 82% of them use at least one prescription drug. The margin of error is 2 percentage points (based on data from “Use of Prescription and Over-the-Counter Medications and Dietary Supplements Among Older Adul

> Announcement in a large department store: “Attention shoppers. Everything in the store is now reduced by 10%, but in one hour all prices will be increased by 10%.” The prices will therefore revert to the original amounts.

> My bank raised its interest rate on savings accounts from 1% to 1.5%, which was a 50% increase.

> A dealer has a new Corvette with a sticker price of $60,000. Because the demand is high and the supply is low, the dealer announces that the actual cost will be 10% more than the sticker price, so the actual cost becomes $66,000.

> Why can it be misleading to give measurements with more precision than is justified by the measurement process?

> Distinguish between accuracy and precision. Give an example of a measurement that is precise but inaccurate and another example of a measurement that is accurate but imprecise.

> Distinguish between the absolute error and the relative error in a measurement. Give an example in which the absolute error is large but the relative error is small and another example in which the absolute error is small but the relative error is large.

> Distinguish between random errors and systematic errors. How can we minimize the effects of random errors? How can we account for the effect of a³systematic error?

> If a killer whale weighing 4000 kg swallows a fish that weighs 2 kg, the whale will weigh 4002 kg.

> Eight years ago, we learned that the age of the earth is 4.543 billion years, so the age of the earth is now 4,543,000,008 years.

> In a USA Today survey, 21% of 144 respondents said that they aspired to have their boss’s job. The margin of error is 7 percentage points.

> The United Nations reported that the global illegal drug trade has a value of $321.6 billion.

> The St. Louis Gateway Arch is 630.2377599694 feet tall.

> The Burj Khalifa in Dubai is 2717 feet tall, making it the world’s tallest building.

> Last year, the population of China was 1,393,783,836.

> Over one full year, there were 33,804 deaths in the United States due to motor vehicle crashes.

> The population of the United States in 1860 was 31,443,321.

> Suppose your weight is 52.55 kilograms. A scale at a health clinic that gives weight measurements to the nearest half kilogram gives your weight as 52¹∕² kilograms. A digital scale at the gym that gives readings to the nearest 0.01 kilogram gives your we

> Suppose your weight is 52.55 kilograms. A scale at a health clinic that gives weight measurements to the nearest half kilogram gives your weight as 53 kilograms. A digital scale at the gym that gives readings to the nearest 0.01 kilogram gives your weigh

> Assume that your statistics professor has a height of exactly 175.2 cm. Assume that this height is measured with a tape measure that can be read to the nearest millimeter (1 mm, or 1/10 cm) and results from two different measurements are reported as 175

> A new Corvette weighs 3440 pounds. A manufacturer’s scale that is accurate to the nearest 10 pounds gives the weight as 3450 pounds, while the U.S. Department of Transportation uses a scale that is accurate to the nearest 0.1 pound and obtains a weight o

> When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 580 peas, and 26% of them were yellow .The margin of error is 4 percentage points. Based on his theory of genetics, Mendel expected that 25% of the offs

> When a model 22F car battery is weighed, the measuring instrument is very precise, and the weight is measured 10 consecutive times. a. All 10 measurements are not likely to be exactly the same; some will be slightly higher than the true value and some lo

> Twenty-five people, including yourself, are to measure the length of a room to the nearest tenth of a millimeter. Assume that everyone uses the same well-calibrated measuring device, such as a tape measure. a. All 25 measurements are not likely to be exa

> The bakery menu claims that there are 12 doughnuts in a bag, but the baker always puts 13 doughnuts (the true value) in each bag.

> The actual (true value) amount of change due after a gallon of milk is purchased is $12.00, but the incorrect amount of $2.00 is given instead.

> The official distance for a marathon is 26 miles 385 yards, or 26.21875 miles, but the organizers of a marathon map a course that is actually 26.34567 miles in length.

> You receive a Visa credit card bill for $512.50, but it includes a charge of $8.00 that was not valid. (That is, the true credit card bill should be $8.00 less than the bill claims.)

> The accuracy of gas pumps is routinely measured by government agencies that collect samples using measuring devices known to be accurate.

> Speeds of cars are recorded by a police officer who uses a radar gun.

> The police commissioner in New York City estimates the annual value of counterfeit goods sold in the city.

> Periodically, a survey is conducted in which subjects are asked if they wash their hands after using a public restroom.

> A USA Today report stated a survey of 22,000 high school students found that 39% of them reported being tired on most school days. The margin of error is less than 0.1 percentage point. Can we safely conclude that fewer than half of all students say they

> After randomly selecting 1009 adults and surveying each of them, a pollster was able to 8 Speaking of Statistics determine that precisely 54% of all American adults are not comfortable having drones make deliveries to them.

> In a survey of randomly selected high school students, the subjects are asked how many cigarettes they smoke each day.

> The health commissioner of Los Angeles estimates the number of cigarettes smoked in her city from data for taxes collected on sales of cigarettes.

> The annual incomes of 200 people are obtained from their tax returns.

> Randomly selected adult subjects are asked to report their total annual income.

> Former New York City Police Commissioner Raymond Kelly criticized the city’s statistics on shootings by claiming that they were being underreported. If shootings were being underreported, is that a random error or a systematic error? Explain.

> A smartphone battery is supposed to provide 3.8 volts. An aftermarket supplier manufactures 5000 replacement batteries and finds that they have a mean output of 3.8 volts, but about half of the batteries supply less than 3.8 volts and half supply more th

> Before taking off, a pilot is supposed to set the aircraft altimeter to the elevation of the airport. A pilot leaves from Denver (altitude 5280 feet) with her altimeter set to 2500 feet. Explain how this affects the altimeter readings throughout the flig

> An IRS agent reviews tax returns to identify the following: (1) mistakes made in calculations and (2) incorrect entries that were intentionally made to lower the tax bill. Discuss whether each problem involves random or systematic errors.

> I used a meter stick to measure the length of my bed to the nearest micrometer.

> In a recent year, the value of cross-border trade in counterfeit and pirated goods was $254.63 billion.

> In an Eagleton Institute poll, surveyed men were asked if they agreed with this statement: “Abortion is a private matter that should be left to women to decide without government intervention.” Among the men who were interviewed by women, 77% agreed wit

> Consider the measurements described in Exercise 5. The relative error that the microbiologist makes in measuring a cell must be less than the relative error that the astronomer makes in measuring a galaxy.

> A microbiologist measures the distance across a red blood cell and an astronomer measures the distance across the Milky Way galaxy. The absolute error that the microbiologist makes in measuring the cell must be less than the absolute error that the astro

> A survey asked people about their party affiliation and recorded the responses as 1 for Democrat, 2 for Republican, 3 for Independent, and 4 for anything else. The survey found that the average (mean) party affiliation is 2.5.

> Explain why temperatures on the Fahrenheit or Celsius scales are at the interval level of measurement while distances are at the ratio level.

> What do we mean by data at the nominal, ordinal, interval, and ratio levels of measurement?

> Distinguish between discrete and continuous data, and give an example of each.

> What is the difference between qualitative data and quantitative data?

> In a clinical trial of a new drug, subjects are placed in groups as follows: Subjects in Group 1 are each given a placebo containing none of the drug; subjects in Group 2 are each given 10-mg doses of the drug; subjects in Group 3 are each given 20-mg do

> Consumer Reports magazine lists a rating of “best buy,” “recommended,” or “not recommended” for each of several different computers.

> The Michelin tire company also rates restaurants, using 1 star, 2 stars, or 3 stars. Many other restaurants are deemed to have quality not good enough to earn any stars, and many others are not judged.