Statistics Questions and Answers fall 2024
In a statistical study what is the difference between an individual and a variable? ** Answ**
An individual is a member of the population of interest. A variable is an aspect of an individual
subject or object being measured
Are data at the nominal level of measurement quantitative or qualitative? ** Answ**
qualitative
What is the difference between a parameter and a statistic? ** Answ** A parameter is a
numerical measurement describing data from a population. A statistic is a numerical
measurement describing data from a sample.
For a set population, does a parameter ever change? ** Answ** never
If there are three different samples of the same size from a set population, is it possible to get
three different values for the same statistic? ** Answ** Data from samples may vary from
sample to sample, and so corresponding sample statistics may vary from sample to sample.
(a) Consider these number assignments for category items describing electronic ways of
expressing personal opinions.
1 = Twitter; 2 = e-mail; 3 = text message; 4 = Facebook; 5 = blog
Are these numerical assignments at the ordinal data level or higher? Explain. ** Answ** No,
they are at the nominal level as there is no apparent ordering in the responses.
(b) Consider these number assignments for category items describing usefulness of customer
service.
1 = not helpful; 2 = somewhat helpful; 3 = very helpful; 4 = extremely helpful
Are these numerical assignments at the ordinal data level? Explain. ** Answ** Yes, the data
has an ordering to its categories.
What about at the interval level or higher? Explain. ** Answ** No, while the data has an
ordering, and the data can be compared to each other, the differences don't mean anything.
What is the average miles per gallon (mpg) for all new hybrid small cars? Using Consumer
Reports, a random sample of such vehicles gave an average of 35.7 mpg.
1) Identify the variable.
2) Is the variable quantitative or qualitative?
3) What is the implied population? ** Answ** 1) miles per gallon
2) quantitative
3) all new hybrid small cars
, Government agencies carefully monitor water quality and its effect on wetlands (Reference:
Environmental Protection Agency Wetland Report EPA 832-R-93-005). Of particular concern is
the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill
fish and wildlife. Twenty-eight samples of water were taken at random from a lake. The nitrogen
concentration (milligrams of nitrogen per liter of water) was determined for each sample.
1) Identify the variable.
2) Is the variable quantitative or qualitative?
3) What is the implied population? ** Answ** 1) nitrogen concentration
2) quantitative
3) the entire lake
Categorize these measurements associated with a robotics company according to level: nominal,
ordinal, interval, or ratio.
1) Salesperson's performance: below average, average, above average.
2) Price of company's stock
3) Names of new products
4) Temperature (°F) in CEO's private office
5) Gross income for each of the past 5 years
6) Color of product packaging ** Answ** 1) ordinal
2) ratio
3) nominal
4) interval
5) ratio
6) nominal
Explain the difference between a stratified sample and a cluster sample. ** Answ** Stratified
sample: random samples from each strata are included
Cluster sample: the clusters to be included are selected at random and then all members of each
selected cluster are included.
Explain the difference between a simple random sample and a systematic sample. ** Answ**
Simple Random sample: every sample of size n has an equal chance of being included.
Systematic sample: the only samples possible are those including every kth item from the
random starting position.
Consider the students in your statistics class as the population and suppose they are seated in four
rows of 10 students each. To select a sample, toss a coin. If it comes up heads, you use the 20
students sitting in the first two rows as your sample. If it comes up tails, you use the 20 students
sitting in the last two rows as your sample.
(a) Does every student have an equal chance of being selected for the sample? Explain.
(b) Is it possible to include students sitting in row 3 with students sitting in row 2 in your
sample? Is your sample a simple random sample? Explain.
(c) Describe a process you could use to get a simple random sample of size 20 from a class of
size 40. ** Answ** a) Yes, your seating location and the randomized coin flip ensure equal
chances of being selected.
In a statistical study what is the difference between an individual and a variable? ** Answ**
An individual is a member of the population of interest. A variable is an aspect of an individual
subject or object being measured
Are data at the nominal level of measurement quantitative or qualitative? ** Answ**
qualitative
What is the difference between a parameter and a statistic? ** Answ** A parameter is a
numerical measurement describing data from a population. A statistic is a numerical
measurement describing data from a sample.
For a set population, does a parameter ever change? ** Answ** never
If there are three different samples of the same size from a set population, is it possible to get
three different values for the same statistic? ** Answ** Data from samples may vary from
sample to sample, and so corresponding sample statistics may vary from sample to sample.
(a) Consider these number assignments for category items describing electronic ways of
expressing personal opinions.
1 = Twitter; 2 = e-mail; 3 = text message; 4 = Facebook; 5 = blog
Are these numerical assignments at the ordinal data level or higher? Explain. ** Answ** No,
they are at the nominal level as there is no apparent ordering in the responses.
(b) Consider these number assignments for category items describing usefulness of customer
service.
1 = not helpful; 2 = somewhat helpful; 3 = very helpful; 4 = extremely helpful
Are these numerical assignments at the ordinal data level? Explain. ** Answ** Yes, the data
has an ordering to its categories.
What about at the interval level or higher? Explain. ** Answ** No, while the data has an
ordering, and the data can be compared to each other, the differences don't mean anything.
What is the average miles per gallon (mpg) for all new hybrid small cars? Using Consumer
Reports, a random sample of such vehicles gave an average of 35.7 mpg.
1) Identify the variable.
2) Is the variable quantitative or qualitative?
3) What is the implied population? ** Answ** 1) miles per gallon
2) quantitative
3) all new hybrid small cars
, Government agencies carefully monitor water quality and its effect on wetlands (Reference:
Environmental Protection Agency Wetland Report EPA 832-R-93-005). Of particular concern is
the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill
fish and wildlife. Twenty-eight samples of water were taken at random from a lake. The nitrogen
concentration (milligrams of nitrogen per liter of water) was determined for each sample.
1) Identify the variable.
2) Is the variable quantitative or qualitative?
3) What is the implied population? ** Answ** 1) nitrogen concentration
2) quantitative
3) the entire lake
Categorize these measurements associated with a robotics company according to level: nominal,
ordinal, interval, or ratio.
1) Salesperson's performance: below average, average, above average.
2) Price of company's stock
3) Names of new products
4) Temperature (°F) in CEO's private office
5) Gross income for each of the past 5 years
6) Color of product packaging ** Answ** 1) ordinal
2) ratio
3) nominal
4) interval
5) ratio
6) nominal
Explain the difference between a stratified sample and a cluster sample. ** Answ** Stratified
sample: random samples from each strata are included
Cluster sample: the clusters to be included are selected at random and then all members of each
selected cluster are included.
Explain the difference between a simple random sample and a systematic sample. ** Answ**
Simple Random sample: every sample of size n has an equal chance of being included.
Systematic sample: the only samples possible are those including every kth item from the
random starting position.
Consider the students in your statistics class as the population and suppose they are seated in four
rows of 10 students each. To select a sample, toss a coin. If it comes up heads, you use the 20
students sitting in the first two rows as your sample. If it comes up tails, you use the 20 students
sitting in the last two rows as your sample.
(a) Does every student have an equal chance of being selected for the sample? Explain.
(b) Is it possible to include students sitting in row 3 with students sitting in row 2 in your
sample? Is your sample a simple random sample? Explain.
(c) Describe a process you could use to get a simple random sample of size 20 from a class of
size 40. ** Answ** a) Yes, your seating location and the randomized coin flip ensure equal
chances of being selected.
