Question
MATH399 Applied Managerial Statistics
Week 1 Assignment Sampling and Parameters
QuestionRaymond wants to estimate the percentage of parents
that use cloth diapers. He asks a randomly selected group of 200
parents whether or not they use cloth diapers. What is the data?
the percentage of all parents that use cloth diapers
the 200 people surveyed
all parents that use cloth diapers
the percentage of surveyed parents that use cloth diapers
specific “yes” or “no” responses to the survey
QuestionPatrick wants to estimate the percentage of parents
that use cloth diapers. He asks a randomly selected group of 125
parents whether or not they use cloth diapers. What is the
statistic?
the 125 people surveyed
the percentage of all parents that use cloth diapers
the percentage of surveyed parents that use cloth diapers
all parents that use cloth diapers
specific “yes” or “no” responses to the survey
QuestionNick wants to estimate the percentage of homeowners
that own at least one dog. He surveys 150randomly selected
individuals to determine whether or not they own dogs. What is the
sample?
the percentage of surveyed homeowners that own at least one
dog
all homeowners
the percentage of all homeowners that own at least one dog
specific responses to the survey
the 150 homeowners surveyed
QuestionWhat is all individuals, objects, or measurements
whose properties are being studied?
population
variable
statistic
data
QuestionWhen considering different sampling methods, cluster
sampling includes the steps: _______.
use simple random sampling to select a set of groups; every
individual in the chosen groups is included in the sample
list the members of the population; use simple random
sampling to select a starting point in the population; let k =
(number of individuals in the population)/(number of individuals
needed in the sample); choose every kth individual in the list
starting with the one that was randomly selected
divide the population into groups; use simple random sampling
to identify a proportionate number of individuals from each group
identify individuals of the population that are easily
accessible; obtain data from these individuals
QuestionTrue or False?In reference to different sampling
methods, cluster sampling includes the steps: use simple random
sampling to select a set of groups; every individual in the chosen
groups is included in the sample.
True
False
QuestionIs the statement below true or false?A variable is a
characteristic of interest for each person or object in a
population.
True
False
QuestionMatthew wants to estimate the mean height of students
attending his college. He records the heights of 100 randomly
selected students attending the college. What is the population?
the mean height of the randomly selected students
the mean height of all students attending the college
the 100 randomly selected students
all the students attending the college
the heights of the randomly selected students
QuestionThere are 6000 people who attended a political debate
at a convention center. There are three candidates who are
participating in the debate – Mr. Smith, Mr. Jones, or Ms. Roberts.
You want to find out which candidate is most popular amongst the
people attending. You ask 500 people as they walk into the
convention center.
Which represents the population in this scenario?
The three candidates – Mr. Smith, Mr. Jones, and Ms. Roberts
The 500 people surveyed
The 6000 people attending the debate
Everyone who has been the convention center that month
QuestionYou want to find the average test score of the
students in every math class in 11th grade. There are 15math
classes in 11th grade. You survey the scores of 7 math classes, and
you calculate that the average test score is 83%.
Which of the following represent the sample and the parameter
in this scenario?
Sample: 7 math classes
Parameter: There is no parameter in this scenario.
Sample: 7 math classes
Parameter: the average test score of 83%
Sample: 15 math classes
Parameter: There is no parameter in this scenario.
Sample: 15 math classes
Parameter: the average test score of 83%
Statistics and Data
The science of statistics deals with the collection,
analysis, interpretation, and presentation of data. We see and use
data in our everyday lives.
In statistics, we generally want to study a population. A
population is a total collection of persons, things, or objects
under study. Gathering information about an entire population often
costs too much or is virtually impossible. Instead, we collect a
sample of the population or a smaller portion of the larger
population. This is usually easier to do, and gives us a good idea
of what’s going on in the population. A sample should have the same
characteristics as the population it is representing.
Data are information about populations or samples. Generally,
there are unknown characteristics, or variables, about a population
that we wish to know. To obtain this information, we collect data
by sampling some members of a population. Once collected, the data
are used as the actual values of the variables. Data may be numbers
(quantitative data) or they may be words (qualitative data).
Example 1
You want to determine the overall grade point average (GPA)
at your school. There are 1800 students at your school. Since you
want to collect data about all of the students, all 1800 students
is the population. The variable is overall GPA at your school.
But, it would be difficult to ask every single one of the
1800 students in your school about his/her GPA. So, it would make
sense to gain information from a smaller group of students who
attend your school. So, you survey 200 random students. This
portion of the population is called the sample.
The grade point averages of the students surveyed is the data
collected.
A statistic and a parameter are both descriptions of groups,
but they represent different groups.
A parameter is a number that is a property of the population.
Sometimes, when the population is small enough, there is no need to
take a sample, and so determining a parameter is easier and a more
accurate reflection of the population. A statistic is a number that
represents a property of the sample. The statistic is an estimate
of a population parameter.
Example 2
There are 100 Senators in the U.S. Senate. 20 Senators voted
against a bill last month. This number is an example of a
parameter, because it is a number that represents the whole
population.
There are 12,000 people at a football stadium. You want to
determine the average number of miles people drove to the stadium.
Instead of surveying the whole populationof 12,000 people, you
randomly choose 1000 people as your sample. The average number of
miles driven to the stadium by the sample is an example of a
statistic.
Key Terms
•
Population: entire group of people/things under research
•
Sample: a subset, or smaller portion of the population
•
Variable: element, feature, or factor that is liable to vary or
change
•
Data: values of variables
•
Parameter: a number that is a property of the population
•
Statistic: a number that represents a property of the sample
QuestionAnnie wants to estimate the percentage of homeowners
that own at least one dog. She surveys 75randomly selected
individuals to determine whether or not they own dogs. What is the
population?
the 75 homeowners surveyed
specific responses to the survey
the percentage of surveyed homeowners that own at least one
dog
the percentage of all homeowners that own at least one dog
all homeowners
QuestionIn reference to different sampling methods, is the
following statement true or false?
Cluster sampling includes the steps: divide the population
into groups; use simple random sampling to identify a proportionate
number of individuals from each group.
True
False
QuestionIn reference to different sampling methods, is the
following statement true or false?
Systematic sampling includes the steps: identify individuals
of the population that are easily accessible; obtain data from
these individuals.
True
False
QuestionRaymond wants to estimate the percentage of parents
that use cloth diapers. He asks a randomly selected group of 200
parents whether or not they use cloth diapers. What is the
parameter?
the percentage of surveyed parents that use cloth diapers
the 200 people surveyed
specific “yes” or “no” responses to the survey
the number of parents
the percentage of all parents that use cloth diapers
QuestionIs the statement below true or false?
Data is a subset of the population studied.
True
False
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