Chapter One, Probability and Statistics: 11th Grade

Stratified, cluster

For ___ sampling, each of the strata contains members with a certain characteristic (for example a particular age group). In contrast, ___ consist of geographic groupings, and each cluster should consist of members with all of the characteristics (for examples, all age age groups).

Ratio

Identify the Level of Measurement: The average ticket prices for 10 rock concerts in 2003 are listed.

Ratio

Identify the Level of Measurement: The lengths (in inches) of a sample of striped bass caught in Maryland water are listed. 16, 17.25, 19, 18.75, 21, 20.3, 19.8, 24, 21.82

Nominal

Identify the Level of Measurement: The region representing the top salesperson in a corporation for the past six years is given. Southeast, Northwest, Northeast, Southeast, Southwest, Southwest

Nominal

Identify the Level of Measurement: The three political parties in the 108th Congress are listed. Republican, Democrat, Independent

Ordinal

Identify the Level of Measurement: The top five musical artists on July 23, 2003 by box office rank are listed. 1.) The Eagle 2.) Dave Matthews Band 3.) The Dixie Chicks 4.) Fleetwood Mac 5.) Cher

Ordinal

Identify the Level of Measurement: The top five teams in the final college football poll released on January 4, 2004 are listed. 1.) USC 2.) LSU 3.) Oklahoma 4.) Ohio 5.) Miami

Cluster because there are naturally occurring subgroups and geography is involved. Bias is that there are more areas than just the ones chosen, and their needs might be different.

Identify the Sampling Technique and Bias: After a hurricane, a disaster area is divided into 200 equal grids. Thirty of the grids are selected, and every occupied household in the grid is interviewed to help focus relief effort on what residents require the most.

Stratified because there are two starts that share a similar characteristic and are randomly selected. Bias is that the people are only 65 and older.

Identify the Sampling Technique and Bias: Chosen at random, 500 rural and 500 urban persons age 65 or older were asked about their health and experience with prescription.

Systematic because each part is assigned a number. Bias is that you are selecting the 20th part, what if the 18th was faulty?

Identify the Sampling Technique and Bias: For quality assurance, every twentieth engine part is selected from an assembly line and is tested for durability.

Convenience because only the first 32 teachers are asked. Bias those teachers are not representative of all teachers.

Identify the Sampling Technique and Bias: Questioning teachers as they left a faculty lounge, a researcher asked 32 teachers about their teaching styles and grading methods.

Simple Random because each telephone number has an equal chance of being dialed. The bias is that only homes with telephones will be sampled.

Identify the Sampling Technique and Bias: Using random digit dialing, researchers called 1599 people and asked what obstacles (such as childcare) kept them from exercising.

Collection of all United States households

Identify the population: A survey of 2104 household in the United States found that 65% subscribe to cable television.

Collection of the 2104 household in the United States surveyed

Identify the sample: A survey of 2104 household in the United States found that 65% subscribe to cable television.

Population because all the people in the company are included in the data

Is it a population or sample, explain why: The annual salary for each employee at a company.

Sample because not all cars are being recorded

Is it a population or sample, explain why: The speed of every fifth car passing a police speed trap.

Yes

Is the question biased: Why is drinking fruit juice bad for you?

Nominal Level of Measurement

Is when data is at the Qualitative level only. Data at this level are categorized by using names, labels, or qualities; no mathematical computations can be done at this level

Qualitative Data

Letters or words; consists of attributes, labels, or nonnumerical entries

Ordinal

Level of Measurement: Put in a category and put in order.

Interval

Level of Measurement: Put in a category, put in order, and find differences between values.

Ratio

Level of Measurement: Put in a category, put in order, find differences between values, and find ratios of values.

Nominal

Level of Measurement: Put in a category.

An association exists between U.S. women and being the primary investor in their household

Make an inference based on the results: A survey of 546 women found that more than 56% are the primary investor in their household.

Vacationers from the U.S. spend at least $2000 on vacation

Make an inference based on the results: A survey of 791 vacationers from the United States found that they planned on spending at least $2000 for their next vacation

Simulation because the situation is impractical

Method of Data Collection Needed and Why: A study of how fast a virus would spread in a metropolitan area.

Census because you are studying all members

Method of Data Collection Needed and Why: A study of the ages of the 535 members of the U.S. Congress.

Observational because you want to observe and measure certain measurements of part of a population

Method of Data Collection Needed and Why: A study of the effect of a product's warning label to determine whether consumers still buy the product.

Experiment because you want to measure the effect of a treatment in the human digestive system

Method of Data Collection Needed and Why: A study of the effect on the human digestive system of potato chops made with a fat substitute.

Quantitative Data

Numbers; consists of numerical measurements or counts

Parameter because all magazines were included

Parameter or a statistic, explain: In a recent year, the interest category for 12% of all new magazines was sports.

Statistic because not all high schoolers were surveyed

Parameter or a statistic, explain: In a survey of a sample of high school students, 43% said that their mother has taught them the most about managing money.

Parameter vs. Statistic

What terms correlates to All vs. Some

Quantitative

Qualitative or Quantitative: The daily low temperatures for the month of January.

Qualitative

Qualitative or Quantitative: The player numbers for a soccer team.

Quantitative

Qualitative or Quantitative: The scores of a class on an accounting exam.

Qualitative

Qualitative or Quantitative: The telephone numbers in a telephone directory.

Use a Simulation

The use of a mathematical or physical model to reproduce the conditions of a situation or process

True

True of False: A sample is a subset of a population

Cluster

Type of Sampling: Divide the population into groups and select all of the members in one or more (but not all) of the clusters

Systematic

Type of Sampling: Each member of the population is assigned a number

Random

Type of Sampling: Every member of the population has an equal chance of being selected; select individuals

Simple Random

Type of Sampling: Every possible sample of the same size has the same chance of being selected; selecting a sample

Convenience

Type of Sampling: Leads to biased studies

Stratified

Type of Sampling: When it's important for the sample to have members from each segment of the population

Sampling

A count or measure of part of a population

Parameter

A numerical description of a population characteristic

Statistic

A numerical description of a sample characteristic

Observational Study

A researcher observes and measures characteristics of interest of part of a population; write down what you observe

Sample

A subset of a population

Scales

A timeline and a thermometer are both examples of ____.

Perform and Experiment

A treatment is applied to part of a population and responses are observed

Biased

A type of sample that is not representative of the population or which is drawn

Inherent Zero

A zero that implies "none"

Use a Survey

An investigation of one or more characteristics of a population. Most often, surveys are carried out on people by asking them questions

Data

Consists of information coming from observations, counts, measurements, or responses

Ratio Level of Measurement

Data are similar to the data at the interval level, with the added property that a zero entry is an inherent zero. A ratio of two data values can be formed so that one data value can be expressed as a multiple of another data value.

Interval Level of Measurement

Data at the quantitative level. Data can be ordered and you can calculate meaningful differences. At the interval level, zero is a position on a scale and the entry is not an inherent zero

Ordinal Level of Measurement

Data at this level can be Qualitative or Quantitative; data at this level can be arranged in order but has no meaningful differences

Quantitative

The Interval Level involves what type of data?

Qualitative

The Nominal Level involves what type of data?

Qualitative, Quantitative

The Ordinal Level involves what type of data?

Quantitative

The Ratio Level involves what type of data?

Descriptive Statistics

The branch of statistics that involves the organizing, summarizing, and displaying the data; describe

Inferential Statistics

The branch of statistics that involves using a sample to draw conclusions about a population. A basic tool in the study of this type of statistics is probability; infee

Population

The collection of all outcomes, responses, measurements, or counts that are of interest

Observational, experimental

The difference between an observational study and an experimental is that, in an ___ study, a researcher does not influence the responses, whereas in an ___, a researcher deliberately applies a treatment before observing the responses.

Nominal

The following are an example of what type of measurement: Social Security numbers, numbers on sports jerseys, phone numbers

Statistics

The science of collecting, organizing analyzing, and interpreting data in order to make decisions

56% are the primary investor in their household

Which part represents the descriptive branch of statistics: A survey of 546 women found that more than 56% are the primary investor in their household.

Spending at least $2000

Which part represents the descriptive branch of statistics: A survey of 791 vacationers from the United States found that they planned on spending at least $2000 for their next vacation

Because it is impractical to obtain all of the data from a population

Why is a sample used more often than a population?

Stratified, cluster

With ____ samples, some of the members of each group are used. In a ___ sampling, all of the members of one or more groups are used.