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.