Question 1

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate.
-1 - School lunches cost $1.10 at district grade schools, and they cost $1.75 at district high schools.
2 - Sue Ellen is on an 1100 calorie a day diet, and Samuel is on an 1800 calorie a day diet.

Accepted Answer

Both statements involve quantities that can be meaningfully compared using ratios. The cost of school lunches and daily calorie intake are both numerical values that can be divided to find a ratio, indicating how one value relates to the other in terms of size or magnitude.

Question 2

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio)is most appropriate.
-The sample of spheres categorized from softest to hardest

Accepted Answer

The categories of softest to hardest imply a natural ordering, making it an example of ordinal measurement. Nominal measurement would simply label the spheres, interval measurement would require a consistent unit of measurement for the softness/hardness, and ratio measurement would require a true zero point (which does not exist in this case).

Question 3

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate.
-1 - At The Gap, Buffy has a credit card balance of $556, and Rosa has a credit line of $111.
2 - Juan saved $435 last month, and Ian saved $321 last month.

Accepted Answer

A ratio of the measurements is meaningful in the context of comparing savings because it reflects the relative amount saved by each person, which is a direct comparison of similar quantities. In contrast, comparing a credit card balance to a credit line does not provide meaningful information about relative financial status or behavior.

Question 4

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate.
-1 - Kesha scored 720 on the verbal SAT, and Salam scored 680.
2 - The lowest temperature in Normal, IL last winter was 12 F, and the lowest temperature in Rockford, IL last
Winter was -8 F.

Accepted Answer

The answer of Two statements are given. Identify the statement...

Question 5

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate.
-1 - The average score for the lowest-scoring third grade in the district was the 31 st percentile, and the highest w. 78th percentile.
2 - Pieta's mother goes to work at 9:00 AM, and Emily's mother goes to work at 7:00 AM.

Accepted Answer

Percentiles and times are not measurements that can be meaningfully compared using ratios.

Question 6

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate.
-1 - The tallest girl on the team is $6 ^ { \prime } 1 ^ { \prime \prime }$, and the shortest is $5 ^ { \prime } 2 ^ { \prime \prime }$.
2 - The length of the rectangle is $17.2 \mathrm {~cm}$, and the width is $8.2 \mathrm {~cm}$.

Accepted Answer

Both statements involve measurements of length, so a ratio of the measurements is meaningful.

Question 7

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio)is most appropriate.
-Salaries of college professors

Accepted Answer

Salaries of college professors can be ordered, have a meaningful zero point (indicating no salary), and the differences between salaries are meaningful, which are characteristics of the ratio level of measurement.

Question 8

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio)is most appropriate.
-Students' grades, A, B, or C, on a test

Accepted Answer

Students' grades (A, B, or C) on a test are best described as ordinal data because they can be ranked (A is higher than B, and B is higher than C), but the differences between the grades are not necessarily consistent or measurable in a meaningful way, unlike interval or ratio data.

Question 9

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate.
-1 - The lowest IQ score in the class is 112 , and the highest is $141 .$
2 - The oldest teacher at the university is 71 years old, and the youngest is 25 .

Accepted Answer

Ratios are meaningful for age because age is a ratio scale with a true zero point (birth). IQ scores do not have a true zero, so ratios are not meaningful for them.

Question 10

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate.
-1 - I ate twice as many tacos as you did.
2 - I love tacos twice as much as you do.

Accepted Answer

The first statement allows for a quantifiable comparison (a ratio of the number of tacos eaten), while the second statement involves subjective feelings, which cannot be measured or compared in a meaningful ratio.

Question 11

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio)is most appropriate.
-Ages of survey respondents

Accepted Answer

Ages of survey respondents are measured on a ratio scale because they have a meaningful zero point (birth) and the distances between age values are consistent and meaningful.

Question 12

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio)is most appropriate.
-The temperatures of eight different plastic spheres

Accepted Answer

Temperature measurements are at the interval level because they have meaningful differences between values, but zero does not indicate an absence of temperature (it's arbitrary, as in the Celsius and Fahrenheit scales).

Question 13

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio)is most appropriate.
-Amount of fat (in grams)in cookies

Accepted Answer

The amount of fat in grams in cookies is a ratio level of measurement because it has a natural zero point (0 grams of fat means no fat) and allows for comparisons of absolute quantities.

Question 14

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio)is most appropriate.
-The subjects in which college students major

Accepted Answer

The subjects in which college students major are categorized without any inherent order, making the nominal level of measurement most appropriate. Nominal data classify observations into mutually exclusive categories solely for identification or naming.

Question 15

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate.
-1 - Kim pulled weeds at the rate of twenty weeds per minute, and Jorge pulled 18 weeds per minute.
2 - AnnaLisa held her breath for one minute 27 seconds, and Marissa held her breath for one minute 41 seconds.

Accepted Answer

Both statements involve ratios that are meaningful because they compare quantities in similar units: weeds per minute for the first statement and time (minutes and seconds) for the second statement.

Question 16

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio)is most appropriate.
-Survey responses of"good", "better", "best"

Accepted Answer

These survey responses indicate a clear order (good < better < best) but do not specify the exact differences between these categories, making them ordinal.

Question 17

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio)is most appropriate.
-Temperatures of the ocean at various depths

Accepted Answer

Temperatures of the ocean at various depths are measured on an interval scale because they can be ordered, have meaningful differences between values, but do not have a true zero point (where zero does not mean the absence of temperature).

Question 18

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate.
-1 - Kasheta ran the race in 22.3 sec, and Louisa ran the same race in 26.4 sec.
2 - Juan gets out of school at 2:45 PM, and Aito gets out of school at 3:15 PM.

Accepted Answer

The time it takes to run a race is a quantitative measurement that can be directly compared or expressed as a ratio (e.g., Kasheta's time to Louisa's time). The school dismissal times are points in time, not durations, so a ratio of these times isn't meaningful.

Question 19

Two statements are given. Identify 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, and the unfertilized grass grew 1.8 inches in the same week.
2 - The single-stage model rocket went up 287 ft, and the two-stage model rocket went up 412 ft.

Accepted Answer

Ratios of measurements are meaningful in both cases because they compare similar quantities (growth in inches for grass, and height in feet for rockets), allowing for a direct comparison of their relative sizes or performances.

Question 20

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio)is most appropriate.
-Nationalities of survey respondents

Accepted Answer

Nationalities of survey respondents are categorized without any inherent order or ranking, making the nominal level of measurement most appropriate. This level is used for labeling variables without any quantitative value.

Quiz 2: Measurement in Statistics

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. -The sample of spheres categorized from softest to hardest

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate. -1 - At The Gap, Buffy has a credit card balance of $556, and Rosa has a credit line of $111. 2 - Juan saved $435 last month, and Ian saved $321 last month.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. -Salaries of college professors

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. -Students' grades, A, B, or C, on a test

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate. -1 - The lowest IQ score in the class is 112 , and the highest is $141 .$ 2 - The oldest teacher at the university is 71 years old, and the youngest is 25 .

Two statements are given. Identify the statement for which a ratio of the measurements is meaningful. State "Neither" or "Both" if appropriate. -1 - I ate twice as many tacos as you did. 2 - I love tacos twice as much as you do.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. -Ages of survey respondents

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. -The temperatures of eight different plastic spheres

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. -Amount of fat (in grams) in cookies

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. -The subjects in which college students major

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. -Survey responses of"good", "better", "best"

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. -Temperatures of the ocean at various depths

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. -Nationalities of survey respondents