Explain what is meant by the term population.

A population is the total collection of objects that are of interest in a statistical study.

Explain what is meant by the term sample.

is any subset or sub collection of the population, including the case that the sample consists of the whole population.

Explain how a sample differs from a population.

A sample, being a subset, is typically smaller than the population. In a statistical study, all elements of a sample are available for observation, which is not typically the case for a population

Explain what is meant by the term sample data.

The measurements of sample elements

Explain what a parameter is.

A parameter is a value describing a characteristic of a population. In a statistical study the value of a parameter is typically unknown.

Explain what a statistic is.

a collection of methods for collecting, displaying, analyzing, and drawing conclusions from data.

Give an example of a population and two different characteristics that may be of interest.

All currently registered students at a particular college form a population. Two population characteristics of interest could be the average GPA and the proportion of students over 23 years.

descriptive statistics

the branch of statistics that involves organizing, displaying, and describing data.

Inferential statistics

the branch of statistics that involves drawing conclusions about a population based on information contained in a sample taken from that population.

Identify each of the following data sets as either a population or a sample: The grade point averages (GPAs) of all students at a college.

Population.

Identify each of the following data sets as either a population or a sample: The GPAs of a randomly selected group of students on a college campus.

Sample

Identify each of the following data sets as either a population or a sample: The ages of the nine Supreme Court Justices of the United States on January 1, 1842.

Population

Identify each of the following data sets as either a population or a sample: gender of every second customer who enters a movie theater.

Sample

The lengths of Atlantic croakers caught on a fishing trip to the beach.

Sample

Identify the following measures as either quantitative or qualitative: The 30 high-temperature readings of the last 30 days.

Quantitative

Identify the following measures as either quantitative or qualitative: The scores of 40 students on an English test.

Quantitative

Identify the following measures as either quantitative or qualitative: The blood types of 120 teachers in a middle school.

Qualitative

Identify the following measures as either quantitative or qualitative: The last four digits of social security numbers of all students in a class.

Qualitative

Identify the following measures as either quantitative or qualitative: The numbers on the jerseys of 53 football players on a team.

Qualitative

Identify the following measures as either quantitative or qualitative: The genders of the first 40 newborns in a hospital one year.

Qualitative

Identify the following measures as either quantitative or qualitative: natural hair color of 20 randomly selected fashion models.

Qualitative

Identify the following measures as either quantitative or qualitative: ages of 20 randomly selected fashion models.

Quantitative

Identify the following measures as either quantitative or qualitative: The fuel economy in miles per gallon of 20 new cars purchased last month.

Quantitative

Identify the following measures as either quantitative or qualitative: political affiliation of 500 randomly selected voters.

Qualitative

A researcher wishes to estimate the average amount spent per person by visitors to a theme park. He takes a random sample of forty visitors and obtains an average of $28 per person. What is the population of interest?

all visitors to the theme park

A researcher wishes to estimate the average amount spent per person by visitors to a theme park. He takes a random sample of forty visitors and obtains an average of $28 per person. What is the parameter of interest?

the true average amount spent per person by all visitors to the theme park

A researcher wishes to estimate the average amount spent per person by visitors to a theme park. He takes a random sample of forty visitors and obtains an average of $28 per person. Based on this sample, do we know the average amount spent per person by visitors to the park? Explain fully.

No. The researcher only sampled 40 visitors. The $28 is the sample average (statistic), which is used to estimate the true average for all visitors (parameter). We don't know the exact population average.

A researcher wishes to estimate the average weight of newborns in South America in the last five years. He takes a random sample of 235 newborns and obtains an average of 3.27 kilograms. What is the population of interest?

The weight of newborns in South America in the last five years.

A researcher wishes to estimate the average weight of newborns in South America in the last five years. He takes a random sample of 235 newborns and obtains an average of 3.27 kilograms. What is the parameter of interest?

the true average weight of newborns in South America in the last 5 years.

A researcher wishes to estimate the average weight of newborns in South America in the last five years. He takes a random sample of 235 newborns and obtains an average of 3.27 kilograms. Based on this sample, do we know the average weight of newborns in South America? Explain fully.

No, not exactly, but we know the approximate value of the average.

A researcher wishes to estimate the proportion of all adults who own a cell phone. He takes a random sample of 1,572 adults; 1,298 of them own a cell phone, hence 1298∕1572 ≈ .83 or about 83% own a cell phone. What is the population of interest?

All adults

A researcher wishes to estimate the proportion of all adults who own a cell phone. He takes a random sample of 1,572 adults; 1,298 of them own a cell phone, hence 1298∕1572 ≈ .83 or about 83% own a cell phone. What is the parameter of interest?

The true proportion of all adults who own a cell phone.

A researcher wishes to estimate the proportion of all adults who own a cell phone. He takes a random sample of 1,572 adults; 1,298 of them own a cell phone, hence 1298∕1572 ≈ .83 or about 83% own a cell phone. What is the statistic involved?

The proportion computed from the sample, .83.

Based on this sample, do we know the proportion of all adults who own a cell phone? Explain fully.

No, since we only sampled 1,572 adults, we don't know the exact proportion for all adults.

A sociologist wishes to estimate the proportion of all adults in a certain region who have never married. In a random sample of 1,320 adults, 145 have never married, hence 145∕1320 ≈ .11 or about 11% have never married. What is the population of interest?

All adults in a certain region

A sociologist wishes to estimate the proportion of all adults in a certain region who have never married. In a random sample of 1,320 adults, 145 have never married, hence 145∕1320 ≈ .11 or about 11% have never married. What is the parameter of interest?

The true proportion of all adults in a certain region who have never married

A sociologist wishes to estimate the proportion of all adults in a certain region who have never married. In a random sample of 1,320 adults, 145 have never married, hence 145∕1320 ≈ .11 or about 11% have never married. What is the statistic involved?

The proportion computed from the sample, 0.11

A sociologist wishes to estimate the proportion of all adults in a certain region who have never married. In a random sample of 1,320 adults, 145 have never married, hence 145∕1320 ≈ .11 or about 11% have never married. on this sample, do we know the proportion of all adults who have never married? Explain fully.

No, not exactly, but we know the approximate value of the proportion.