07 Jan the number of parents

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