MATH 2001 Statistics - Homework Chapter 1

The years that a television show on a particular network won an award for best drama series are: 1951, 1962, 1963, 1968, 1990, 1994, 2001, 2008 and 2012. Determine the level of measurement of the data set. Explain your reasoning.

Interval. The data can be ordered and differences between data entries are meaningful, but a zero entry is not an inherent zero.

The jersey numbers for players on a soccer team are: 13, 7, 48, 6, 20, 12, 9, 16, 17, 19, 22, 24, 5, 18, 3, 15, 14, 4, 8, 27, 32, 36, 30, 34, 26, 67 and 11. Identify the level of measurement of the data set. Explain your reasoning.

Nominal. The data are categorized using numbers, but no mathematical computations can be made.

Determine whether the data set is a population or a sample. Explain your reasoning. The salary of each teacher in a school.

Population, because it is a collection of salaries for all teachers int he school.

Why is a sample used more often than a population?

It is usually impossible to count the entire population

The list of books that your friend read for school for the past five months is: Threat Vector; Kiss the Dead; The Racketeer; Private London; and Gone Girl. Identify the level of measurement of the data set. Explain your reasoning.

Nominal. The data are categorized using names, labels, or qualities, but the data cannot be ranked or arranged in order.

Determine whether the underlined value is a parameter or a statistic. The average score for a class of 28 students taking a calculus midterm exam was __72%__.

Parameter

Determine whether the data set is a population or a sample. Explain your reasoning. The number of cars for 10 households in a neighborhood of 30 households.

Sample, because the collection of the number of cars for 10 households is a subset of all households in the neighborhood.

In a poll, 1,004 men in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Among respondents, 46% said that they were if favor. Identify the population and the sample.

Population: All men in the country Sample: The 1,004 men selected

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Wait time at doctors office.

The variable is QUANTITATIVE because wait times are NUMERICAL MEASUREMENTS.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Favorite song.

The variable is qualitative because a favorite song describes an attribute or characteristic.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Amount of money won in a lottery.

The variable is quantitative because amount of money is found by measuring or counting.

Determine whether the data set is a population or a sample. Explain your reasoning. The salary of 17 teachers in a school.

This is a sample, because it is a collection of salaries for some teachers in the school.

What is the difference between a parameter and a statistic?

A parameter is a numerical descriptions of a POPULATION characteristic. A statistic is a numerical description of a SAMPLE characteristic.

How is a sample related to a population?

A sample is a subset of a population.

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A population is the collection of some outcomes, responses, or counts that are of interest.

False. A population is the collection of ALL outcomes, responses, or counts that are of interest.

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A statistic is a measure that describes a population characteristic.

False. A statistic is a measure that describes a sample characteristic.

Determine whether the data set is a population or a sample. Explain your reasoning. The age of each member of the House of Representatives.

Population, because it is a collection of ages for all members of the House of Representatives.

Determine whether the data set is a population or a sample. Explain your reasoning. The salary of each baseball player in a league.

Population, because it is a collection of salaries for all baseball players in the league.

A polling organization contacts 1886 adult women who are 30 to 70 years of age and live int eh United States and asks whether or not they had received a mammogram during the past year. Identify the population and the sample.

Population: Adult women who are 30 to 70 years of age and live in the United States. Sample: The 1886 adult women who are 30 to 70 years of age and live in the United States.

Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. In a phone survey of 100 random homes in a country, __21%__ of families had garages.

Statistic, because the data set of 100 random homes is a sample.

Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. After a tornado, a disaster area is divided into 150 equal grids. Forty of the grids are selected, and every occupied household in the grid is interviewed to help focus relief efforts on what residents require the most.

TYPE: Cluster sampling is used, since the disaster area is divided into grids, and some of those grids are selected and everyone in those grids is interviewed. BIAS: Certain grids may have been much more severely damaged than others. The grids that are selected may not be representative in terms of damage. Certain grids may have been much more severely damaged than others. Severely damaged grids may have fewer occupied households.

Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. Assume the population of interest is the student body at a university. Questioning students as they leave a university parking lot, a researcher asks 384 students about their eating habits.

TYPE: Convenience sampling is used, because students are chosen due to convenience of location. BIAS: Because of the personal nature of the question, students may not answer honestly. The sample only consists of members of the population that are easy to get. These members may not be representative of the population.

Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. In 1965, researchers used random digit dialing to call 1400 people and ask what obstacles kept them from exercising.

TYPE: Simple random sampling was used, since each number had an equal chance of being dialed, so all samples of 1400 phone numbers had an equal chance of being selected. BIAS: Individuals may not have been available when the researchers called. Individuals may have refused to participate int eh sample. Telephone sampling only includes people who had telephones.

Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. Tomatoes are planted on a 51-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest.

TYPE: Stratified Sampling is used, since the field is divided into subplots and a random sample is taken from each subplot. BIAS: Certain subplots may have more or fewer tomato plants than others. Samples from these subplots may bias the overall sample.

Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. Every sixteenth person entering a sporting goods store is asked to choose his or her favorite sport from a list of five different sports that includes a description of each.

TYPE: Systematic sampling is used, because every sixteenth person is selected. BIAS: IF there is a regular pattern to the people entering the sporting goods store, the sample may not be representative. The wording of the question may direct respondents towards a particular sport.

Determine whether the underlined number describes a population parameter or a sample statistic. Explain your reasoning. A survey of 2207 adults in a country found that __84%__ think that militant terrorists are a major threat to the well-being of their country.

The number is a sample statistic because it describes the people in a sample, which is a subset of all the people in the country.

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sample statistic will not change from sample to sample.

The statement is false. A sample statistic CAN change from sample to sample.

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. It is impossible for the Census Bureau to obtain all the census data about the population of the United States.

The statement is true.