Question 1

Identify the potential error in recording arrival times for interstate highway trips as random or systematic.

Accepted Answer

The answer of Identify the potential error in recording arrival...

Question 2

Convert 5.65 to a percent.

Accepted Answer

To convert a number to a percent, multiply it by 100. Thus, 5.65 * 100 = 565%.

Question 3

A pharmacist puts 32 pills into a prescription order that calls for 30 pills. What is the absolute error?

Accepted Answer

The absolute error is the difference between the measured value and the true value, which is 32 pills - 30 pills = 2 pills.

Question 4

Select the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate.
-1 The fertilized grass grew 2.9 inches in a week; the unfertilized grass grew 1.8 inches in the same week.
2 The single-stage model rocket went up 287 ft; the two-stage model rocket went up 412 ft.

Accepted Answer

Both statements involve measurements where a ratio is meaningful, as they compare growth and height, respectively, which are quantitative and can be expressed as ratios.

Question 5

A part of the CPI table is given below: $$\begin{array} { l | l | l | l | l | l } 
\text { Year } & 1975 & 1980 & 1985 & 1990 & 1995 \
\hline \text { CPI } & 53.8 & 82.4 & 107.6 & 130.7 & 152.4
\end{array}$$ Suppose an actuary's salary was $86,000 in 1995. What would the salary have to have been in 1975 if it had just kept up with inflation (round to the nearest $1000)?

Accepted Answer

To find the equivalent salary in 1975, use the formula: Salary_1975 = (CPI_1975 / CPI_1995) * Salary_1995. Plugging in the values: (53.8 / 152.4) * 86,000 ≈ $30,000.

Question 6

The approximate value of π is 3.1415927. Which of the following experimentally determined values is the most precise?

Accepted Answer

The value 3.412114 has the most decimal places, indicating it is the most precise measurement.

Question 7

A computer uses voice recognition software. Identify a misinterpreted word as a systematic or random error.

Accepted Answer

Systematic errors are caused by a consistent problem in the system, such as a faulty sensor or a software bug. In this case, the voice recognition software is consistently misinterpreting a particular word, which suggests that there is a systematic error in the system.

Question 8

Research shows that 14% of 6th graders in K-6 schools have tried cigarettes and 61% of 7th graders in 8-9 or 7-9 middle schools have tried cigarettes. What is the absolute increase, to the nearest percent?

Accepted Answer

The absolute increase is calculated by subtracting the percentage of 6th graders who have tried cigarettes from the percentage of 7th graders who have tried cigarettes: 61% - 14% = 47%.

Question 9

A cook estimates one-third of a cup in a cup measuring cup marked in quarters. Assuming that the cook knows how big 1/3 is, relative to 1/4 and 1/2, identify the potential measurement error as systematic or random.

Accepted Answer

The answer of A cook estimates one-third of a cup...

Question 10

Brand of basketball shoes worn by a team.

Accepted Answer

The brand of basketball shoes is a qualitative variable because it describes a category or characteristic rather than a numerical value.

Question 11

The pickup time of an answering machine is set at 5 rings, but the machine picks up after 4 rings. What is the relative error?

Accepted Answer

The answer of The pickup time of an answering machine...

Question 12

Research shows that 14.3% of persons 20-25 years old vote and 59.9% of persons 60-65 years old vote. What is the absolute increase from the younger group to the older group, to the nearest point.

Accepted Answer

The absolute increase is calculated by subtracting the percentage of the younger group from the older group: 59.9% - 14.3% = 45.6%, which rounds to 46 points.

Question 13

Rather than use the two scoops of coffee recommended by the manufacturer, a coffee aficionado uses three scoops of coffee per pot. What is the relative error?

Accepted Answer

The answer of Rather than use the two scoops of...

Question 14

Compared with a stopwatch that gives readings as --. - seconds, a stopwatch that gives readings as --. -- seconds is

Accepted Answer

A stopwatch that gives readings to two decimal places (--. -- seconds) is more precise because it can measure smaller intervals of time. However, this increased precision does not necessarily mean it is more accurate, as accuracy depends on how close the measurements are to the true value.

Question 15

A person is always late for class. Identify the potential error as random or systematic.

Accepted Answer

The person is always late for class, indicating a consistent pattern or cause for their lateness. This suggests a systematic error, as it is not a random occurrence.

Question 16

Suppose that the cost of a statistics text was $55 in 1985 and is $90 in 2000. What is the 'Statistics Text Index' number, rounded to the nearest tenth, for the 1985 edition with the 2000 price as the reference value?

Accepted Answer

The index number is calculated as (Price in 1985 / Price in 2000) * 100 = (55 / 90) * 100 = 61.1.

Question 17

A botany student counted 11 blades of grass in one square centimeter of lawn and measured the lawn as a rectangle 61 m by 31 m. She reported that there were 208,010,000 blades of grass in the lawn. The precision of her conclusion

Accepted Answer

The precision of her conclusion is excessive because she calculated the number of blades of grass to a very precise number (208,010,000) based on an initial count of only 11 blades per square centimeter, which is not precise enough to justify such an exact total count.

Question 18

Convert 13% to decimal form.

Accepted Answer

The answer of Convert 13% to decimal form.
...

Question 19

Select the description that most completely classifies the given variable
-Number of wins by the NFL teams in the NFC Central division

Accepted Answer

The number of wins is a quantitative variable because it represents a countable quantity. It is also a ratio variable because it has a true zero point (a team can have zero wins) and the differences between values are meaningful.

Question 20

The size of an e-mail file is stated as 210 kB, but the file size is actually 220.5 kB. What is the absolute error?

Accepted Answer

The answer of The size of an e-mail file is...

Quiz 2: Measurement in Statistics