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statistical reasoning for everyday life
Statistical Reasoning For Everyday Life 5th Edition Jeff Bennett, William Briggs, Mario Triola - Solutions
What do we mean when we say that distribution is skewed? Briefly describe the basic difference between a distribution that is skewed to the right and a distribution that is skewed to the left.
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?
As this text goes to press, the government is considering but has not yet made a change to using the chained CPI. Has such a change happened yet? Investigate the current status of the debate over replacing the standard CPI with the chained CPI for the purposes of setting tax rates and
Briefly describe how you find quartiles and percentiles for a data set.
Adamson Company manufactures four lines of garden tools. As a result of activity analysis, the accounting department has identified eight activity cost pools. Each of the product lines is produced in large batches, with the whole factory devoted to one product at a time. Classify each of the
What do we mean when we say that distribution is symmetric? Can asymmetric distribution have more than one mode?
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?
Because using the chained CPI would lead to a slower rise in the income thresholds for various tax rates, conservatives often claim that this change would mean a “stealth tax increase.” Similarly, because the change would reduce the annual increases in cost-of-living adjustments, liberals often
What is the level of measurement of the values described in Exercise 1 (nominal, ordinal, interval, or ratio)?Exercise 1 Braking reaction times of 36 randomly selected licensed drivers are measured. Are those data considered quantitative or qualitative? ³ If quantitative, are those values
What are outliers? Describe the effects of outliers on mean, median, and mode.
Briefly distinguish between the following measures of variation: range, five-number summary, and standard deviation. Which one(s) can be represented with a boxplot?
Distinguish between a uniform distribution and a distribution with one or more modes. What do we call distributions with one, two, and three modes?
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?
Find examples in your own spending or the spending of friends and family members of substitution effects and the purchase of products that were unavailable or of lower quality a few years ago. Overall, do you think these examples support the claim that the CPI overstates the effects of inflation?
Braking reaction times of 36 randomly selected licensed drivers are measured. Are those data considered quantitative or qualitative? ³ If quantitative, are those values continuous or discrete?
Define and distinguish among mean, median, and mode.
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.
Find a recent news article that includes a line chart. Briefly explain what the line chart shows, and discuss whether it helps make the point of the news article. Are the labels clear? Is the line chart a time-series graph? Explain.
Find a recent news article that includes a histogram. Briefly explain what the histogram shows, and discuss whether it helps make the point of the news article. Are the labels clear? Is the histogram a time-series graph? Explain.
Find an example in the news of a graphic that combines two or more of the basic graphic types. Briefly explain what the graphic is showing, and discuss its effectiveness.
Find an example of a threedimensional graphic in a recent news report. Are three dimensions needed, or are they included for cosmetic reasons? Comment on the effectiveness of the display. Could another type of graphic have been used to depict the same data?
Find a recent news article that includes a pie chart. Briefly discuss the effectiveness of the pie chart. For example, would it be better if the data were displayed in a bar graph rather than a pie chart? Could the pie chart be improved in other ways?
In a simple random sample of adults, the pulse rate is measured for each subject.Qualitative versus Quantitative Data. In Exercises, determine whether the data described are qualitative or quantitative, and explain why.
Braking reaction times of 36 randomly selected licensed drivers are measured and 20 of them are greater than 1.9 seconds. What is the percentage of reaction times greater than 1.9 seconds?
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 astronomer makes in measuring the Milky Way.Does
Congress and the President are almost always proposing new changes in tax laws. Research one recent proposed change, providing a brief summary of the proposal and of the arguments for and against it. Do you personally support the proposal? Why or why not?
The price of a gallon of gas tripled, so it increased by 300%.Does It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive answers, so your explanation is more
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.Does It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly
ZIP codes are quantitative data because, in general, lower numbers are in the east and higher numbers are in the west.Does It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these
Recorded survey results include the states in which respondents reside. Are those data considered quantitative or qualitative, and what is their level of measurement (nominal, ordinal, interval, or ratio)?
Find examples in your own spending or the spending of friends and family members of substitution effects and the purchase of products that were unavailable or of lower quality a few years ago. Overall, do you think these examples support the claim that the CPI overstates the effects of inflation?
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.Does It Make Sense? For Exercises, determine whether the statement
The CPI doubled from 1983 to 2006, so the price of gasoline also doubled over that time period.Does It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive answers,
Los Angeles reached a temperature of 100°F today, which was twice as hot as the 50°F in Denver.Does It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive
In a Gallup poll of 1038 adults, 5% of the respondents said that second-hand smoke is not at all harmful. How many respondents said that second-hand smoke is not at all harmful?
In a recent year, the value of cross-border trade in counterfeit and pirated goods was $254.63 billionDoes It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive
Because using the chained CPI would lead to a slower rise in the income thresholds for various tax rates, conservatives often claim that this change would mean a “stealth tax increase.” Similarly, because the change would reduce the annual increases in cost-of-living adjustments, liberals often
My bank raised its interest rate on savings accounts from 1% to 1.5%, which was a 50% increase.Does It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive answers,
My salary has remained the same for the past 10³years, but my standard of living has fallen.Does It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive answers,
The year 2050 will be halfway through the twenty-first century.Does It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive answers, so your explanation may be more
Two different students measure the height of an instructor who is actually 178.44 cm tall. The first student obtains a measurement of 178 cm and the second student obtains a measurement of 179.18 cm. Which measurement is more accurate? Which measurement is more precise?
I used a meter stick to measure the length of my bed to the nearest micrometer.
As this text goes to press, the government is considering but has not yet made a change to using the chained CPI. Has such a change happened yet? Investigate the current status of the debate over replacing the standard CPI with the chained CPI for the purposes of setting tax rates and
An announcement in a large department store: “Attention shoppers. Everything in the store is now reduced by10%, but in one hour all prices will be increased by 10%.” The prices will therefore revert to the original amounts.
Adjusted for inflation, today’s price of $100 for that item is lower than the 1980 price of $50.Does It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive
The common blood groups are A, B, AB, and O.Qualitative versus Quantitative Data. In Exercises, determine whether the data described are qualitative or quantitative, and explain why.
The Electronics Company has been in business for five years, and the following table lists the company’s net profit in each of those years. Using the first year as a reference value, find the index number for the net profit in the second year. Year 1 3 4 5 Net profit
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.
In Figure 2.5, notice that the revenue increases and spending savings get larger each year. Discuss why this occurs, focusing on how a change in the CPI compounds over time, much like compound interest on a bank account.Figure 2.5 Deficit Reduction Using a Chained CPI 50 Savings on benefits and
If you spent $12,250 for goods, services, and housing in 2015, what would the same purchases have cost in 2000?Consumer Price Index. In Exercises, use the Consumer Price Index values from Table 2.2. TABLE 2.2 Average Annual Consumer Price Index (1982–1984 =
Express each of the following numbers in the three forms fraction, decimal, and percentage.a. 3/5 b. 0.8 c. 150% d. 25%
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.Does It Make Sense? For, determine whether the statement makes sense (or
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 flight. What kind of error is this?
While most economists believe that the CPI overstates the effects of inflation, a few believe that it actually understates the effects, especially on lower-income people. Research why some economists come to this conclusion, then draw your own conclusion: Does the CPI sometimes understate the
Express the following numbers in the three forms of fraction, decimal, and percentage.a. 275% b. 3.75 c. 0.45 d. 90%
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 than 3.8 volts. Does the error appear to
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 Guilty?” by Brereton and Casper, Law and
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 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 spinning pennies, and 9,197 of those pennies
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 appearance of a job applicant is most
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%?
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).
Using the CPI values from the above table and Table 2.2, determine what a slice of pizza should have cost in 2010 if it cost $1.00 in 1986 and prices had risen with the CPI. What does this tell you about how actual pizza prices changed compared to the CPI?Table 2.2 TABLE 2.2 Average Annual Consumer
Using the CPI values from the above table and Table 2.2, determine what a slice of pizza should have cost in 2014 if it cost $1.35 in 1995 and prices had risen with the CPI. What does this tell you about how actual pizza prices changed compared to the CPI?Table 2.2 TABLE 2.2 Average Annual Consumer
Using the CPI values from the above table and Table 2.2, determine what the subway fare should have cost in 2006 if it cost $2.50 in 2013 and prices had risen with the CPI. What does this tell you about how actual subway fares changed compared to the CPI?Table 2.2 TABLE 2.2 Average Annual
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.
In a comparison of gasoline with different octane ratings, 24 vans are driven with 87 octane gasoline, and 28 sport utility vehicles are driven with 91 octane gasoline. After each vehicle has been driven for 250 miles, the amount of gasoline it consumed is measured.
Police set up a sobriety checkpoint at which every fifth driver is stopped and interviewed.
In one of Mendel’s famous genetics experiments that he conducted with peas, he obtained a sample of offspring peas consisting of 428 green peas and 152 yellow peas. Based on his theories, he expected that 25% of the offspring peas would be yellow.
The Journal of Consumer Research included a report of a study that was conducted to determine whether people have different spending characteristics when they have a $1 bill or when they have four quarters. The subjects were given a choice: keeping the money or spending it on gum or
A medical researcher is conducting a study to test the effectiveness of a drug designed to lower cholesterol levels. She randomly selects a sample of 100 males and 100 females.
Does listening to Beethoven make teenagers more intelligent?
A consumer researcher surveyed customers at a Macy’s store to obtain sample data consisting of the amount of credit card debt that each customer has.
Does the herb echinacea help prevent colds?
A college dean obtains an alphabetical list of all full-time students at her college and she select every 50th name on that list and interviews those students to find the amount of student debt incurred by each of them. She uses the results to estimate the average (mean) amount of student debt
A company is developing a new battery for smartphones, and it is claimed that the new battery lasts significantly longer than those currently in use.
In a Gallup poll of 1059 adults, the interview subjects were selected by using a computer to randomly generate telephone numbers (both land lines and cell phones) that were then called.
Which siding lasts longer on a home: aluminum, vinyl, or wood?
A market researcher surveys 50 randomly selected drivers from each state and obtains the amount that they paid for a gallon of gas at their most recent purchase.
Search the Internet for articles and information about the controversy regarding recovering repressed memories. Briefly summarize one or two of the most interesting cases and, based on what you read, express your own opinion as to whether the allegedly recovered memories are being influenced by
Ethical standards change from era to era. One notoriously unethical case was a study of syphilis conducted in Tuskegee, Alabama, from 1932 to 1972. In this study, African American males were told that they were receiving treatment for syphilis, but in fact, they were not. The researchers’ hidden
Past research often did not conform to today’s ethical standards. In extreme cases, such as research conducted by doctors in Nazi Germany, the researchers sometimes killed the subjects of their experiments. While this past unethical research clearly violated the human rights of the experimental
It sometimes happens that the study is stopped early before its completion. Use the Internet to find an example of such a study. Why was the study stopped? Should it have been stopped, or would it be better to complete the study?
A sample of manufactured air bags is obtained by using a computer to randomly generate a number between 1 and 1000 for each air bag, and the air bag is tested if the generated number is 1000.
Search through recent newspapers or journals and find an example of a statistical study that was observational. Briefly describe the study and summarize its conclusions.
Search through recent newspapers or journals and find an example of a statistical study that involved an experiment. Briefly describe the study and summarize its conclusions.
The U.S. Food and Drug Administration plans to conduct a survey to identify the average (mean) amount of arsenic found in the rice grown on farms located in Arkansas. Arkansas has about 3000 rice farms.a. What would be a practical problem of using a stratified sample consisting of rice obtained
You want to determine the percentage of people in this country with each of the four major blood types (A, B, AB, and O). What would be an effective sampling plan that accounts for differences among ethnic groups?
Search through recent newspapers or journals and find an example of a meta-analysis. Briefly describe the study and summarize its conclusions.
You want to conduct a survey of parents of elementary school students in Minneapolis by using telephone calls instead of personal visits. Assume you have directories listing telephone numbers of all (or almost all) parents at each of the city’s elementary schools. What type of sample should you
You want to determine the average (mean) error of aircraft altimeters when they are tested at a simulated altitude of 1000 feet.a. What could be a potential problem with a systematic sample obtained by selecting every 500th altimeter as the devices come off the assembly line?b. What could be a
Use information available on the website of a polling organization, such as Gallup, Harris, Pew, or Yankelovich, to answer the following questions.a. How exactly is a sample of subjects selected?b. Based on what you have learned, do you think the poll results are reliable? If so, why? If not, why
Use the Bureau of Labor Statistics website to find details on how the bureau chooses the sample of households in its monthly survey. Write a short summary of the procedure. What is the sample size? If the sample size is very large, does that compensate for having a biased sample?
Find a recent news report about a statistical study that you find interesting. Write a short summary of how the sample for the study was chosen, and briefly discuss whether you think the sample was representative of the population under study.
Find a recent news report about an opinion poll carried out by a news organization (such as Gallup, Harris, USA Today, New York Times, or CNN). Briefly describe the sample and how it was chosen. Was the sample chosen in a way that was likely to introduce any bias? Explain.
Find results from a recent poll conducted by a political organization (such as the Republican or Democratic party or an organization that seeks to influence Congress on some particular issue). Briefly describe the sample and how it was chosen. Was the sample chosen in a way that was likely to
What is the difference between qualitative data and quantitative data?
In a Wakefield Research survey, 1003 subjects were asked if they ever hesitated to give a handshake because of a fear of germs. Of these respondents, 41.0% answered “yes.”a. What is the number of respondents who answered “yes”?b. If 24 of the respondents said that they were not sure, what
Discuss the chart in Figure 2.4a. Why does it only show taxpayer income levels from the top 1% to the top 25%? What does it tell us about the relative tax burden on each group shown? Do you think its claim that the “rich pay more” is an honest depiction or a distortion of the facts? Defend your
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