In order to improve reliability:
A. Repeat your measurements several times
B. Take the average of several measurements
C. Use a better instrument
D. Both taking the average of several measurements and using abetter instrument E. Both repeating your measurements several timesand using a better instrument
12. The measured value considers:
A. True value
B. Bias
C. Random error
D. All of the choices are correct.
13. Measuring a healthy lifestyle. You want to measure the“healthiness” of college students’ lifestyles. Give an example of aclearly invalid way to measure healthiness. Then briefly describe ameasurement process that you think is valid.
14. Rates versus counts. Thirty students in my Stat 1350 classlast semester took Test 1 and 25 of them passed the test.Fifty-five students in my Stat 1350 WEB class last semester tookTest 1 and 43 of them passed the test.
(a) More students in my WEB Stat 1350 class passed Test 1 thanin my traditional Stat 1350 class. Why does this NOT show that myWEB students did better than my traditional students?
(b) What is the passing rate (percentage of students whopassed) for each of my Stat 1350 classes?
WEB: __________________________________ Traditional:______________________________
15. Obesity. An article in the June 30, 2010, ColumbusDispatch reported on the prevalence of obesity among adults in the50 states. Based on information in the article, California hasapproximately 6.7 million obese adults, and Texas has approximately5.2 million. On the other hand, Mississippi has a little over730,000 obese adults. Do these numbers make a convincing case thatCalifornia and Texas have a more substantial problem with obesitythan Mississippi?
16. Measuring intelligence. “Intelligence” means somethinglike “general problem-solving ability.” Explain why it is not validto measure intelligence by a test that asks questions such as
Who wrote “The Star-Spangled Banner”?______________________________________________________ Who won thelast soccer World Cup?__________________________________________________________
17. Testing job applicants. The law requires that tests givento job applicants must be shown to be directly job related. TheDepartment of Labor believes that an employment test called theGeneral Aptitude Test Battery (GATB) is valid for a broad range ofjobs. As in the case of the SAT, blacks and Hispanics get loweraverage scores on the GATB than do whites. Describe briefly whatmust be done to establish that the GATB has predictive validity asa measure of future performance on the job.
18. Validity, bias, reliability. This winter I went to a localpharmacy to have my blood pressure measured using a sophisticatedelectronic machine at the front of the store next to the checkoutcounter. Will the measurement of my blood pressure be biased?Reliable? Valid? Explain your answer.
19. More on bias and reliability. You cut 5 pieces of stringhaving these lengths in inches: 2.9 9.5 5.7 4.2 7.6
A subject measures each length by eye. Make up a set ofresults from this activity that matches each of the descriptionsbelow. For simplicity, assume that bias means the same fixed errorevery time rather than an “on the average” error in manymeasurements.
(a) The subject has a bias of 0.5 inch too long and isperfectly reliable. ___________ ___________ ___________ ______________________
(b) The subject has no bias but is not perfectly reliable, sothat the average difference in repeated measurements is 0.5inch.
___________ ___________ ___________ ______________________
(c) A subject measures the first length (true length = 2.9inches) four times by eye. His measurements are 3.0 2.9 3.13.0
What are the four random errors for his measurements?___________ ___________ ___________ ___________
20. The best earphones. You are writing an article for aconsumer magazine based on a survey of the magazine’s readers thatasked about satisfaction with mid-priced earphones for the iPod andiPhone. Of 1648 readers who reported owning the Apple in-earheadphone with remote and mic, 347 gave it an outstanding rating.Only 69 outstanding ratings were given by the 134 readers who ownedKlipsch Image S4i earphones with microphone. Describe anappropriate variable, which can be computed from these counts, tomeasure high satisfaction with a make of earphone. Compute thevalues of this variable for the Apple and Klipsch earphones. Whichbrand has the better high-satisfaction rating?
21. Measuring pulse rate. You want to measure your restingpulse rate. You might count the number of beats in 5 seconds andmultiply by 12 to get beats per minute. Why is this method lessreliable than actually measuring the number of beats in aminute?
22. Measuring crime. Twice each year, the National CrimeVictimization Survey asks a random sample of about 40,000households whether they have been victims of crime and, if so, thedetails. In all, nearly 135,000 people answer these questions peryear. If other people in a household are in the room while oneperson is answering questions, the measurement of, for example,rape and other sexual assaults could be seriously biased. Why?Would the presence of other people lead to over-reporting orunderreporting of sexual assaults?
Lesson 3 – Making Sense of Numbers
23. A survey in a local newspaper stated that of theindividuals who frequent bookstores, 14% were male and 28% werefemale. What is wrong with this picture?
A. Only 42% of the people were surveyed.
B. The percentages only add up to 42%. It should be 100%. C.There were twice as many females surveyed as males. D. 58% do notgo to bookstores.
E. Nothing is wrong with this picture.
24. A newspaper reported "Approximately 17% of all crime takesplace in the months of August and September." What is misleadingabout this statistic?
A. August and September are low points for crimestatistically. B. It does not discuss the other months.
C. August and September make up 1/6 of the year which is 17%.D. None of the choices are correct.
25. Mark has two coupons—one for 10% off and one for $5 off.The store is allowing him to use both. He says to the cashier toapply the coupons in any order she wants because in the end it'sthe same amount off. Is he correct? (Hint: Try doing this for anitem that is $100.)
A. Yes, it doesn't matter the way the coupons areapplied.
B. No, you should apply the 10% off coupon first then applythe $5 off coupon. C. No, you should apply the $5 off coupon thenapply the 10% off coupon.
D. You cannot determine from the information given.
26. When finding the percent change, your denominator shouldbe:
A. Amount of change B. Starting value
C. The smaller value D. The larger value.
27. If an amount increases from 10 to 40 then the percentincrease is:
A. 300% B. 400% C. 40% D. 10%
28. A newspaper reports "The percent decrease in the amount ofwolves is 150%." What does this mean?
A. The amount of wolves has decreased in half.
B. There is 1/3 the amount of wolves that there has beenpreviously. C. This is not possible. "Percent decrease" can't bemore than 100%. D. None of the choices are correct.
29. What percentage of 30 is 40?
A. 133% B. 75% C. 13.3% D. 7.5%
30. The percent increase from 40 to 70 is:
A. 125% B. 75% C. 175% D. 25%
31. In determining if the numbers make sense you should:
A. Look at the context of the numbers and determine if thereis missing information. B. Look for numbers that don't agree asthey should.
C. Compare numbers and look for numbers that are surprisinglylarge or small.
D. All of the choices are correct.
E. None of the choices are correct.
32. Deer in the suburbs. Westchester County is a suburban areacovering 433 square miles immediately north of New York City. Agarden magazine claimed that the county is home to 800,000 deer. Doa calculation that shows this claim to be implausible.
33. Trash at sea? A report on the problem of vacation cruiseships polluting the sea by dumping garbage overboard said:
On a seven-day cruise, a medium-size ship (about 1,000passengers and 1.000 crew members) might accumulate 222,000 coffeecups, 72,000 soda cans, 40,000 beer cans and bottles, and 11,000wine bottles.
Are these numbers plausible? Do some arithmetic to back upyour conclusion. Suppose, for example, that the crew is as large asthe passenger list. How many cups of coffee must each person drinkevery day?
34. Airport delays. An article in a midwestern newspaper aboutflight delays at major airports said: According to a Gannett NewsService study of U.S. airlines’ performance during the past fivemonths,
Chicago’s O’Hare Field scheduled 114,370 flights. Nearly 10percent, 1,136, were canceled.
Check the newspaper’s arithmetic. What percent of scheduledflights from O’Hare were actually canceled?
35. Battered women? A letter to the editor of the New YorkTimes complained about a Times editorial that said “an Americanwoman is beaten by her husband or boyfriend every 15 seconds.” Thewriter of the letter claimed that “at that rate, 21 million womenwould be beaten by their husbands or boyfriends every year. That issimply not the case.” He cited the National Crime VictimizationSurvey, which estimated 56,000 cases of violence against women bytheir husbands and 198,000 by boyfriends or former boyfriends. Thesurvey showed 2.2 million assaults against women in all, most bystrangers or someone the woman knew who was not her past or presenthusband or boyfriend.
(a) First do the arithmetic. Every 15 seconds is 4 per minute.At that rate, how many beatings would take place in an hour? In aday? In a year? Is the letter writer’s arithmetic correct?
(b) Is the letter writer correct to claim that the Timesoverstated the number of cases of domestic violence againstwomen?
36. Stocks go down. On September 29, 2008, the Dow JonesIndustrial Average dropped 778 points from its opening level of11,143. This was the biggest one-day decline ever. By whatpercentage did the Dow drop that day? On October 28, 1929, the DowJones Industrial Average dropped 38 points from its opening levelof 299. By what percentage did the Dow drop that day? This was thesecond-biggest one-day percentage drop ever.
37. Too good to be true? The late English psychologist CyrilBurt was known for his studies of the IQ scores of identical twinswho were raised apart. The high correlation between the IQs ofseparated twins in Burt’s studies pointed to heredity as a majorfactor in IQ. (“Correlation” measures how closely two variables areconnected. We will meet correlation in Chapter 14.) Burt wroteseveral accounts of his work, adding more pairs of twins over time.Here are his reported correlations as he published them:
What is suspicious here?
