Deck 9: Do the Numbers Make Sense

Question 1

The price of gold was $1061 per ounce on December 31 and has risen 14.78 percent since that time. What is the price per ounce now?

A) $1218.
B) $156.82.
C) $1076.
D) $62.

Answer 1

$1218.

Question 2

Following are data on the populations and numbers of death row prisoners for several states.

Which state has the highest number of death row prisoners relative to the size of its population?

A) California
B) Florida
C) Illinois
D) Nevada

Answer 2

Nevada

Question 3

Michelle's income two years ago was $220,000. Last year, her income was $300,000. The percent change in Michelle's income was:

A) 36.4 percent increase.
B) 364 percent increase.
C) 3.64 percent increase.
D) 80 percent increase.
E) None of the above.

Answer 3

36.4 percent increase.

Question 4

A web page headline said, "Winter Storm Jonas Slams the East Coast-Airline Cancels All But 0.1 Percent, or 62, Out of the Scheduled 6000 Flights." The correct percentage canceled was:

A) nearly one-hundredth of 1 percent.
B) nearly 1 percent.
C) nearly 10 percent.
D) nearly 100 percent.

Question 5

The net asset value of a mutual fund has decreased from $2,700 on December 31 to $1,330 now. The percent decrease in value is about:

A) 103 percent.
B) 1.03 percent.
C) 0.507 percent.
D) 50.7 percent.
E) 5.07 percent.

Question 6

Which of the following statements do you think could possibly be true?

A) The number of students enrolled at City College decreased by 103.4% last year.
B) A basketball team took 20 free throws in a game last week and made 72.6% of them.
C) Yesterday, it was 30° (Fahrenheit) in Chicago. Today, it warmed up to 60°. This is a 50% increase in the temperature.
D) My weight decreased by 10% last year but then increased by 10% in the first two months of this year. Thus, my overall weight from the beginning of last year until now is unchanged.
E) None of the above

Question 7

An ad for a new mouth rinse says that it "reduces plaque on teeth by 200%." What does this mean?

A) It means that one-fifth of the plaque is removed because 200/1000 = 0.2, or one-fifth.
B) It's nonsense because plaque is a categorical variable, so percents don't make sense.
C) It means that there is 2 times as much plaque before using the rinse as there is after using it.
D) It's nonsense because removing 100% of the plaque already removes all of it, and you cannot remove more than there was at the beginning.
E) It's nonsense because percents only make sense for counts, and amount of plaque isn't a count.

Question 8

An ad for a new heartburn treatment says that it "reduces heartburn by 300%." What does this mean?

A) It means that there is 3 times as much heartburn before using the treatment as there is after using it.
B) It means there is only seven-tenths as much heartburn after using the treatment because 300/1000 = 0.3, or three-tenths.
C) It's nonsense because removing 100% of the heartburn already removes all of it.
D) It's nonsense because heartburn is a categorical variable, so percents don't make sense.
E) It's nonsense because percents only make sense for counts, and amount of heartburn isn't a count.

Question 9

Before starting a body building program, Joe weighed 185 pounds. At the end of the program, he weighed 202 pounds. This is a percentage gain of:

A) 8.42 percent.
B) 17 percent.
C) 9.19 percent.
D) 0.919 percent.
E) 8.43 percent.

Question 10

The Dow Jones Industrial Average (DJIA) is the most common measure of stock market prices. Suppose that the DJIA starts at 17,149 points and drops 500 points. This is a decrease of:

A) 0.029 percent.
B) 2.9 percent.
C) 29.1 percent.
D) 291 percent.

Question 11

The average wage of production workers (adjusted for the effects of inflation) was $11.08 an hour in 1981 and $10.35 an hour in 1991. In the decade of the 1980s, wages went down by about

A) 73%.
B) 7.3%.
C) 7.0%.
D) 6.6%.

Question 12

In the last half of 2015, the price of Apple, Inc. (AAPL) common stock dropped from $126.60 per share to $105.26 per share. What percent decrease is this?

A) 0.1686 percent.
B) 0.2027 percent.
C) 6.86 percent.
D) 20.27 percent.

Question 13

A 500-point drop in the DJIA was a big drop when the DJIA was at 2246 in October of 1987 and a much smaller drop when the DJIA reached 11,421 in September of 2008. The percent by which stock prices fall is a more meaningful measure. The lesson here is that

A) rates are often more meaningful than counts.
B) it is easy to make a mistake calculating a percent.
C) the DJIA is a categorical variable.
D) confidentiality has been violated.

Question 14

A student reports that, of a simple random sample of 25 college undergraduate students, 18% were working at least two jobs. We know that the student has made a mistake (or maybe really did not conduct the survey). Why?

A) There are 25 students in the sample, so percentages should be multiples of 0.04%.
B) There are 25 students in the sample, so percentages should be multiples of 4%.
C) 18% of 25 students is 4.5 students, and you cannot sample a half of a student.
D) Both A and C are correct.
E) Both B and C are correct.

Question 15

A student reports that, of a simple random sample of 50 college undergraduate students, 21% were taking more than fifteen credit hours. We know that the student has made a mistake (or maybe really did not conduct the survey). Why?

A) There are 50 students in the sample, so percentages should be multiples of 2%.
B) There are 50 students in the sample, so percentages should be multiples of 0.02%.
C) 21% of 50 students is 10.5 students, and you cannot sample a fraction of a student.
D) Both A and C are correct.
E) Both B and C are correct.

Question 16

In 1989, 2.0 billion cigars were smoked in the United States. In 2015, 2.4 billion cigars were smoked. What percentage change is this?

A) 40 percent increase
B) 24 percent increase
C) 20 percent decrease
D) 20 percent increase
E) 120 percent increase

Question 17

According to the FBI Uniform Crime Report, the robbery rate in the United States is 202 per 100,000 people. At that rate, how many robberies would there be in a state the size of Indiana (5.8 million people)?

A) About 1200
B) About 12,000
C) About 120,000
D) About 1,200,000
E) Impossible to say

Question 18

A student reports that, of a simple random sample of 200 college undergraduates, 37% were female and 41% were male. We know that the student has made a mistake because

A) it is highly unlikely that a simple random sample of 200 undergraduates would have as few as 37% females.
B) of the possibility of response error.
C) 37% plus 41% is not 100%.
D) the percentages of males and females would be closer together in a true SRS.
E) a stratified random sample would have been less prone to error.

Question 19

Dr. Stat's library of literary classics includes issues of certain scholarly periodicals. The total number of issues of four such periodicals, together with the percentages of Dr. Stat's entire library that they comprise, are as follows:

Exactly one of the percentages in this table is incorrect. Which is it?

A) 18.6% (Spider-Man)
B) 6.2% (Soldier of Fortune)
C) 3.1% (WWF)
D) 7.0% (Mad)

Question 20

A student reports that, of a simple random sample of 100 college undergraduates, 54% were female and 49% were male. We know that the student has made a mistake because

A) it is highly unlikely that there are more females than males at the college.
B) 54% plus 49% equals 103%, which exceeds 100% (everyone in the sample).
C) the student should've also included graduate students.
D) the percentages of males and females should be further apart.

Question 21

From 2010 to 2015, the average annual profit for Acme Floormat Company has increased from $1.5 million to $10 million.

A) This is an increase of 8.5 percent
B) This is an increase of 85 percent.
C) This is an increase of 850 percent.
D) This is an increase of 56.7 percent.
E) This is an increase of 567 percent.

Question 22

A recent warning from a neighborhood watch group stated that about 29% of all home break-ins occur over the weekend (Saturday and Sunday), so residents should be especially vigilant on weekends.

A) Residents should ensure their homes are more secure on weekends than during weekdays.
B) The neighborhood watch group should increase patrols on weekends.
C) The results are not surprising since two-sevenths is about 28.57%.
D) Both A and B are correct.

Question 23

Which of the following statements do you think could possibly be true?

A) Last year, 60 of the 80 residents in a neighborhood subscribed to the local newspaper, and this year, it is 40 residents who subscribe. This is a 50 percent decrease.
B) A company's annual profits increased by 110 percent over the last decade.
C) A teacher brought 40 calculators to class, and 21 percent of them had dead batteries.
D) The number of violent crimes in the city decreased by 112.46 percent last year.
E) None of the above is true.

Question 24

A newspaper reported that a state agency had reduced its workforce by 15% from 80,000 employees to

A) 12,000 employees.
B) 68,000 employees.
C) 78,800 employees.
D) 73,200 employees.

Question 25

It is thought that 63.7% of the student body owns a school sweatshirt. A student reports that from a simple random sample of 1000 students, 637 own a school sweatshirt.

A) This should be trusted since it matches exactly what was thought.
B) It is highly unlikely that an SRS would yield results exactly matching what was expected.
C) Thus, 6.37% of the sample own a school sweatshirt, which refutes the original thought.
D) The student didn't get IRB approval, so the results are invalid.